A ball is dropped from a height of 36 feet. The quadratic equation
d=1/2 gt^2
is used to calculate the distance (d) the ball has fallen after t seconds. The constant g is the acceleration of gravity, 9.8m/s^2. How long does it take the ball to hit the ground?
A ball in problem 2 is dropped again, from a different height. This time, it takes 3 seconds to hit the ground. How far does it fall?
for 1.
d= 36 ft
g = 9.8
find t.
t=?
plug it in and find the answer
for 2.
t=3
g=9.8
find d
d=?
ball is dropped from a height of 36 feet. The quadratic equation
d=1/2 gt^2
is used to calculate the distance (d) the ball has fallen after t seconds. The constant g is the acceleration of gravity, 9.8m/s^2. How long does it take the ball to hit the ground?
A ball in problem 2 is dropped again, from a different height. This time, it takes 3 seconds to hit the ground. How far does it fall?
To find out how long it takes for the ball to hit the ground in the given scenario, we can use the quadratic equation d = 1/2 gt^2.
Given:
Height (h) = 36 feet
Acceleration due to gravity (g) = 9.8 m/s^2
1. Convert the height to meters:
36 feet = 36 * 0.3048 meters (1 foot = 0.3048 meters)
2. Substitute the values into the quadratic equation:
d = 1/2 * 9.8 * t^2
3. Set d to zero because the ball hits the ground at that distance:
0 = 1/2 * 9.8 * t^2
4. Simplify the equation:
0 = 4.9 * t^2
5. Solve for t by factoring or using the quadratic formula:
t^2 = 0
t = 0 (as the ball starts from rest)
Therefore, it takes 0 seconds for the ball to hit the ground.
For the second problem, where the ball takes 3 seconds to hit the ground:
1. Substitute the given value of t into the quadratic equation:
d = 1/2 * 9.8 * (3)^2
2. Evaluate the expression:
d = 1/2 * 9.8 * 9 = 44.1 meters
Therefore, the ball falls 44.1 meters.
To find the time it takes for the ball to hit the ground, we can use the given quadratic equation:
d = 1/2 * g * t^2
Since we want to find the time (t), we can rearrange the equation to solve for t:
t^2 = (2 * d) / g
Taking the square root of both sides, we get:
t = sqrt((2 * d) / g)
For the first question, the ball is dropped from a height of 36 feet. We need to convert this to meters since the acceleration of gravity is given in m/s^2. 1 foot is approximately equal to 0.3048 meters, so the height in meters would be:
d = 36 feet * 0.3048 meters/foot = 10.9728 meters
Now, we can substitute this value of d and the given acceleration due to gravity (g = 9.8 m/s^2) into the formula to find the time (t):
t = sqrt((2 * 10.9728) / 9.8)
≈ sqrt(2.238)
≈ 1.495 seconds
Therefore, it takes approximately 1.495 seconds for the ball to hit the ground.
For the second question, we are given that the ball takes 3 seconds to hit the ground. We can now use this value of t and the same formula to find the distance (d) the ball falls:
d = 1/2 * g * t^2
= 1/2 * 9.8 * 3^2
= 1/2 * 9.8 * 9
= 44.1 meters
Therefore, the ball falls approximately 44.1 meters.