You toss a tennis ball straight upward. At the moment it leaves your hand it is at a height of 1.3 m above the ground, and it is moving at a speed of 7.4 m/s.
(a) How much time does it take for the tennis ball to reach its maximum height?
(b) What is the maximum height above the ground that the tennis ball reaches?
(c) When the tennis ball is at a height of 2.6 m above the ground, what is its speed?
total energy at launch=total energy at top
1/2 m v^2+ mghi=mgIhmax)
1/2 (7.4^2)+9.8(1.3)=9.8(hmax)
solve for hmax
time?
hmax=hi+vi*time-1/2 g t^2
solve for time t.
To solve this problem, we can use the equations of motion for an object in free fall. The key equations we'll need are:
1. v = u + at (equation 1)
2. s = ut + 1/2at^2 (equation 2)
3. v^2 = u^2 + 2as (equation 3)
where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration (which for objects in free fall near the Earth's surface is -9.8 m/s^2, negative because it acts in the opposite direction to the motion)
- t is the time taken
- s is the displacement
(a) To find the time it takes for the tennis ball to reach its maximum height, we need to find when its velocity becomes zero. We are given the initial velocity and can find the acceleration. Therefore, we can use equation 1:
v = u + at
Plugging in the known values:
0 = 7.4 m/s - 9.8 m/s^2 * t
Rearranging the equation to solve for t:
t = u / a
t = 7.4 m/s / 9.8 m/s^2
Solving for t gives us the time it takes for the tennis ball to reach its maximum height.
(b) To find the maximum height above the ground that the tennis ball reaches, we need to find the displacement at that time. We can use equation 2:
s = ut + 1/2at^2
Plugging in the known values:
s = 1.3 m + 7.4 m/s * t + 1/2 * (-9.8 m/s^2) * t^2
Substituting the value of t we found in part (a), we can solve for s.
(c) To find the speed of the tennis ball when it is at a height of 2.6 m above the ground, we can use equation 3:
v^2 = u^2 + 2as
Rearranging the equation to solve for v:
v = sqrt(u^2 + 2as)
Plugging in the known values:
v = sqrt((7.4 m/s)^2 + 2 * (-9.8 m/s^2) * (2.6 m - 1.3 m))
Solving for v gives us the speed of the tennis ball when it is at a height of 2.6 m above the ground.