1. A penny is dropped from the 82nd Floor Observatory of the Empire State Building. The penny will fall from a height of 320 meter (1,050 feet).
(a) How long will it take to fall?
(b) How fast is it going when it hits the ground?
2. Aim the Mythbuster’s penny gun straight up. The penny is launched at a speed of 64 mph.
(a) How high does the penny go?
(b) How long does the penny stay in the air?
3. The largest drop ride in North America is the Drop Zone, Paramount’s Kings Dominion in Virginia. It is 305 feet tall. Passengers free-fall fro 272 feet (82.9 feet).
(a) How much free-fall time do passengers experience?
(b) How fast are passengers going before braking begins?
4. Joe Kittenger, first man to reach the speed of sound without an aircraft. The speed of sound is 340 m/s.
(a) How long did it take to reach this speed?
(b) How far did he fall?
5. Aroldis Champman, 105 mph fastball. If he threw the ball straight up into the air,
(a) how high would it go?
(b) when would it come back down to him?
6. Kadour Ziani (5’10”) holds the world record for the highest vertical leap, 60 inches. FYI: Michael Jordan’s best vertical leap was 48 inches.
(a) Calculate Kadour’s takeoff speed.
(b) How long does he stay in the air?
7. The tallest building in the world is the Burj Khalifia in Dubai, United Arab Emirates, 828 m (2,717 feet). How long would it take King Kong to fall from the top of this one?
8. In a scientific test conducted in Arizona, a special cannon called HARP shot a projectile straight up to an altitude of 1.8x105 m. What was the projectile's initial speed?
9. Cliff divers jump from heights up to 30 meters (95 feet). How fast are they going when they hit the water?
10. If the Moon were to stop orbiting the Earth it would fall towards it. The Moon is 384,504 m from the Earth
(a) How long would it take to hit the Earth?
(b) How fast would it be going?
1. The Bugatti Veyron can go from zero to 60 mph in 2.5 seconds.
(a) How many meters does it travel during the 2.5-s period?
(b) What is the Bugatti¡¦s rate of acceleration?
2. A bullet traveling 220 m/s strikes a tree and penetrates 4.33 cm before stopping.
(a) Find the average acceleration of the bullet.
(b) Find the time it takes to stop.
3. Rocket-powered sleds are used to test the responses of humans to acceleration. Starting from rest, these sleds can reach a speed of 444 m/s in 1.8 seconds.
(a) Calculate the acceleration of these sleds.
(b) How far do these sleds travel during the 1.8-s of acceleration?
4. The highest speed ever achieved on a bicycle was 149.6 miles per hour. If this bicycle could slow down at a rate of -3 m/s2,
(a) how long would it take to stop?
(b) how many meters would it need to stop?
BONUS
A driver of car going 55 mph suddenly sees a deer 40 m in the road ahead. It takes him 0.75 s to apply the brakes. He slams on the brakes and starts to slow down at -10 m/s2.
„h How far does he travel before deceleration?
„h How long will it take him to stop?
„h During deceleration, how far does the car go?
„h Does the car hit the deer?
1. (a) To find the time it takes for the penny to fall, we can use the equation:
t = √(2h/g)
where h is the height (320 meters) and g is the acceleration due to gravity (9.8 m/s^2).
Plug in the values:
t = √(2 * 320 / 9.8)
Calculating the expression:
t ≈ √(64.64)
t ≈ 8.04 seconds
Therefore, it takes approximately 8.04 seconds for the penny to fall.
(b) To find the speed of the penny when it hits the ground, we can use the equation:
v = gt
where v is the speed, g is the acceleration due to gravity (9.8 m/s^2), and t is the time (8.04 seconds) from part (a).
Plug in the values:
v = 9.8 * 8.04
Calculating the expression:
v ≈ 79.8 m/s.
Therefore, the speed of the penny when it hits the ground is approximately 79.8 m/s.
2. (a) To find the maximum height of the penny, we can use the equation:
h = (v^2) / (2g)
where h is the height, v is the initial velocity (64 mph, which needs to be converted to m/s), and g is the acceleration due to gravity (9.8 m/s^2).
First, let's convert 64 mph to m/s:
64 mph ≈ 28.65 m/s
Now, let's plug in the values:
h = (28.65^2) / (2 * 9.8)
Calculating the expression:
h ≈ 42.42 meters.
Therefore, the penny goes up to a height of approximately 42.42 meters.
(b) To find the time the penny stays in the air, we can use the equation:
t = v / g
where t is the time, v is the initial velocity (28.65 m/s), and g is the acceleration due to gravity (9.8 m/s^2).
Plug in the values:
t = 28.65 / 9.8
Calculating the expression:
t ≈ 2.93 seconds.
Therefore, the penny stays in the air for approximately 2.93 seconds.
3. (a) To find the free-fall time, we can use the equation:
t = √(2h/g)
where h is the height of free fall (82.9 feet = 25.2 meters) and g is the acceleration due to gravity (9.8 m/s^2).
Plug in the values:
t = √(2 * 25.2 / 9.8)
Calculating the expression:
t ≈ √(5.14)
t ≈ 2.27 seconds
Therefore, passengers experience approximately 2.27 seconds of free-fall time.
(b) To find the speed of passengers before braking begins, we can use the equation:
v = gt
where v is the speed, g is the acceleration due to gravity (9.8 m/s^2), and t is the time from part (a) (2.27 seconds).
Plug in the values:
v = 9.8 * 2.27
Calculating the expression:
v ≈ 22.25 m/s
Therefore, passengers are going approximately 22.25 m/s before braking begins.
4. (a) To find the time it took for Joe Kittenger to reach the speed of sound, we need more information.
To answer these physics questions, we can use the principles of kinematics and the equations of motion. The two main equations of motion we'll need are:
1) Distance = Initial velocity × Time + 0.5 × Acceleration × Time^2
2) Final velocity = Initial velocity + Acceleration × Time
Let's go through each question and solve them step by step:
1. A penny is dropped from the 82nd Floor Observatory of the Empire State Building. The penny will fall from a height of 320 meters (1,050 feet).
(a) To find the time it takes to fall, we can use the equation of motion mentioned above. In this case, the initial velocity is 0 since the penny is dropped. The acceleration due to gravity is approximately 9.8 m/s^2.
Using the first equation of motion:
Distance = Initial velocity × Time + 0.5 × Acceleration × Time^2
Simplifying the equation for initial velocity = 0:
Distance = 0.5 × Acceleration × Time^2
Plugging in the values:
320 = 0.5 × 9.8 × Time^2
Solving for time, we get:
Time = sqrt(2 × Distance / Acceleration)
Time = sqrt(2 × 320 / 9.8)
Time ≈ 8.03 seconds
(b) To find the final velocity, we can use the second equation of motion mentioned above. Since the penny is only affected by gravity, the acceleration remains the same.
Using the second equation of motion:
Final velocity = Initial velocity + Acceleration × Time
Since the initial velocity is 0, the equation simplifies to:
Final velocity = Acceleration × Time
Plugging in the values:
Final velocity = 9.8 × 8.03
Final velocity ≈ 78.83 m/s
2. Aim the Mythbuster’s penny gun straight up. The penny is launched at a speed of 64 mph.
(a) To find how high the penny goes, we need to calculate the maximum height using the given initial velocity. The acceleration due to gravity remains the same.
Convert the initial velocity from mph to m/s:
Initial velocity = 64 mph × 0.44704 m/s
Initial velocity ≈ 28.96 m/s
Now, we can use the first equation of motion mentioned above to solve for the maximum height. We assume the final velocity when the penny reaches its highest point is 0.
Using the first equation of motion:
Distance = Initial velocity × Time + 0.5 × Acceleration × Time^2
At the maximum height, the distance is the unknown we're looking for. The acceleration due to gravity remains the same.
Since we're looking for the maximum height, we can set the final velocity to 0:
0 = Initial velocity + Acceleration × Time
Plugging in the values:
0 = 28.96 - 9.8 × Time
Time = 28.96 / 9.8 ≈ 2.96 seconds (to reach maximum height)
Now we can calculate the maximum height:
Distance = Initial velocity × Time + 0.5 × Acceleration × Time^2
Distance = 28.96 × 2.96 + 0.5 × 9.8 × (2.96)^2
Distance ≈ 42.5814 meters
(b) To find the total time the penny stays in the air, we double the time it takes to reach the maximum height and add the time it takes to fall back down to the ground. So the total time is approximately 2 × 2.96 seconds = 5.92 seconds.
3. The largest drop ride in North America is the Drop Zone, Paramount’s Kings Dominion in Virginia. It is 305 feet tall. Passengers free-fall from 272 feet (82.9 feet).
(a) To find the free-fall time, we can use the first equation of motion. The acceleration due to gravity is approximately 9.8 m/s^2.
Using the first equation of motion:
Distance = Initial velocity × Time + 0.5 × Acceleration × Time^2
Since the initial velocity is 0, the equation simplifies to:
Distance = 0.5 × Acceleration × Time^2
Plugging in the values:
82.9 = 0.5 × 9.8 × Time^2
Solving for time, we get:
Time = sqrt(2 × Distance / Acceleration)
Time = sqrt(2 × 82.9 / 9.8)
Time ≈ 2.88 seconds
(b) To find the initial velocity before braking begins, we can use the second equation of motion.
Using the second equation of motion:
Final velocity = Initial velocity + Acceleration × Time
Since the final velocity is 0 (at the moment braking begins), the equation simplifies to:
0 = Initial velocity + Acceleration × Time
Plugging in the values:
0 = Initial velocity + 9.8 × 2.88
Initial velocity = -9.8 × 2.88 (negative sign indicates the direction)
Initial velocity ≈ -28.22 m/s
We will continue with the remaining questions in the following response.