An astronaut stands on the edge of a lunar crater and throws a half-eaten Twinkie horizontally with a velocity of 5.00 m/s. The floor of the crater is 100.0 m below the astronaut. What horizontal distance will the Twinkie travel before hitting the floor of the crater? (The acceleration of gravity on the moon is 1/6" that of the Earth). (155.3 ml) . Show solution.
how long does it take to fall 100m?
1/2 (9.81/6) t^2 = 100
t = 11.06 s
d = vt = 5.00 * 11.06 = ____ m
where does the 155.3 mi come into the picture?
Well, let me calculate that for you!
Since the acceleration of gravity on the moon is 1/6th that of Earth's, we can say the acceleration of gravity on the moon is approximately 1.67 m/s² (1/6 * 9.8 m/s²).
Now, let's break down the problem. The astronaut throws the Twinkie horizontally, so its initial vertical velocity is 0 m/s (since it is thrown horizontally).
We know the initial velocity in the horizontal direction is 5.00 m/s. We want to find the horizontal distance the Twinkie will travel before hitting the floor, so we need to find the time it takes to hit the floor.
To find the time, we can use the equation y = y₀ + v₀yt + 0.5at², where
- y is the total vertical displacement (100.0 m)
- y₀ is the initial vertical position (0 m)
- v₀y is the initial vertical velocity (0 m/s)
- a is the acceleration in the vertical direction (-1.67 m/s²)
- t is the time taken (we don't know this yet)
Rearranging the equation, we have 100.0 m = 0.5(-1.67 m/s²)t².
Simplifying, we get -0.835t² = 100.0.
Dividing both sides by -0.835, we have t² = -100.0 / -0.835.
Solving for t, we find t = sqrt(120.48) = 10.98 s (approx).
Now that we have the time, we can find the horizontal distance using the equation x = v₀xt, where
- x is the horizontal distance (we want to find this)
- v₀x is the initial horizontal velocity (5.00 m/s)
- t is the time taken (10.98 s)
Plugging in the values, we get x = (5.00 m/s) * (10.98 s) = 54.9 m (approx).
So, the Twinkie will travel approximately 54.9 meters horizontally before hitting the floor of the crater.
And remember, on the way down, it's not the fall that kills you, it's the sudden stop at the end!
To solve this problem, we can use the kinematic equations of motion.
Given:
Initial velocity (Vi) = 5.00 m/s
Vertical displacement (Δy) = -100.0 m (negative because it is below)
Acceleration due to gravity (g) = (1/6) * 9.8 m/s^2 (as given, on the moon)
We need to find the horizontal distance traveled by the Twinkie before hitting the floor of the crater.
Step 1: Calculate the time it takes for the Twinkie to fall vertically to the floor of the crater.
We can use the equation:
Δy = Viy * t + (1/2) * (g) * t^2
Where:
Δy = -100.0 m
Viy = 0 (since the Twinkie was thrown horizontally)
g = (1/6) * 9.8 m/s^2
Plugging in the values:
-100.0 = 0 * t + (1/2) * (1/6) * 9.8 * t^2
-100.0 = (1/12) * 9.8 * t^2
Step 2: Solve for time (t) by rearranging the equation:
t^2 = (12 * -100.0) / 9.8
t^2 = -122.45
Since time cannot be negative, we discard the negative value, and we get:
t = sqrt(122.45)
t ≈ 11.06 seconds
Step 3: Calculate the horizontal distance traveled (x) by the Twinkie using the equation:
x = Vix * t
Where:
Vix = 5.00 m/s (initial horizontal velocity)
t = 11.06 seconds (from step 2)
Plugging in the values:
x ≈ 5.00 * 11.06
x ≈ 55.3 meters
So, the horizontal distance the Twinkie will travel before hitting the floor of the crater is approximately 55.3 meters.
To solve this problem, we need to apply the principles of projectile motion. Let's break it down into the horizontal and vertical components.
First, let's determine the time it takes for the Twinkie to hit the floor of the crater. Since the Twinkie is only influenced by the vertical component, we can use the equation:
h = (1/2) * g * t^2
Where:
h is the vertical distance (100.0 m)
g is the acceleration due to gravity on the moon (1/6 * 9.8 m/s^2)
t is the time it takes for the Twinkie to hit the floor (unknown)
By plugging in the given values, we can solve for t:
100.0 = (1/2) * (1/6 * 9.8) * t^2
Simplifying this equation gives:
16.3 = t^2
t ≈ 4.03 seconds (approximately)
Next, let's determine the horizontal distance traveled by the Twinkie. Since there is no horizontal acceleration, the horizontal velocity remains constant at 5.00 m/s. We can use the equation:
d = v * t
Where:
d is the horizontal distance (unknown)
v is the horizontal velocity (5.00 m/s)
t is the time it takes for the Twinkie to hit the floor (4.03 seconds)
Plugging in the given values, we can solve for d:
d = 5.00 * 4.03
d ≈ 20.15 meters (approximately)
So, the horizontal distance the Twinkie will travel before hitting the floor of the crater is approximately 20.15 meters.