A student drops a ball from the top of a tall building; the ball takes 2.8 s to reach the ground.
1. what was the ball's speed just before hitting the ground?
2. What is the height of the building?
help please?
assuming it drops from rest you know:
vo=0
t=2.8
a=9.8 (gravity assuming down is +)
v=?
use the equation v=vot+at^2
then you want to find height.
x= vot+.5at^2
Sure! I can help you step by step.
To find the answers to your questions, we can use the equations of motion for an object in free fall.
1. To find the ball's speed just before hitting the ground, we can use the equation: v = u + gt, where:
- v is the final velocity (which is the speed just before hitting the ground),
- u is the initial velocity (which is 0, since the ball is dropped and not thrown),
- g is the acceleration due to gravity (which is approximately 9.8 m/s^2),
- t is the time taken for the ball to reach the ground (which is 2.8 s).
Plugging in the values into the equation, we get:
v = 0 + (9.8 m/s^2)(2.8 s)
2. To find the height of the building, we can use the equation: h = (1/2)gt^2, where:
- h is the height of the building,
- g is the acceleration due to gravity (approximately 9.8 m/s^2),
- t is the time taken for the ball to reach the ground (which is 2.8 s).
Plugging in the values into the equation, we get:
h = (1/2)(9.8 m/s^2)(2.8 s)^2
Now we can calculate the answers. Let's start with the first question.
1. To find the final velocity (v):
v = 0 + (9.8 m/s^2)(2.8 s)
Calculating the equation:
v = 0 + (9.8)(2.8)
v = 27.44 m/s
Therefore, the ball's speed just before hitting the ground is 27.44 m/s.
Now let's move on to the second question.
2. To find the height of the building (h):
h = (1/2)(9.8 m/s^2)(2.8 s)^2
Calculating the equation:
h = (0.5)(9.8)(2.8)^2
h = 38.808 m
Therefore, the height of the building is approximately 38.808 meters.
I hope this helps! Let me know if you have any more questions.
Certainly! Let's break down each question step by step.
1. To find the ball's speed just before hitting the ground, we can use the equation for free fall motion:
v = g * t
where v is the final velocity, g is the acceleration due to gravity, and t is the time taken to reach the ground.
In this case, the acceleration due to gravity (g) is approximately 9.8 m/s^2, and the time (t) taken is 2.8 s.
So, we can calculate the final velocity (v) as:
v = 9.8 m/s^2 * 2.8 s
Therefore, the ball's speed just before hitting the ground is approximately 27.44 m/s.
2. To find the height of the building, we need to use the equation of motion for free fall:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity, and t is the time taken to reach the ground.
We know that g is approximately 9.8 m/s^2, and t is 2.8 s.
Plugging in the values, we get:
h = (1/2) * 9.8 m/s^2 * (2.8 s)^2
Therefore, the height of the building is approximately 38.808 meters.
Please note that these calculations assume there is no air resistance affecting the motion of the ball.