A tennis ball is tossed up off a building with a velocity of 22m/s. It takes 6.4s to reach the ground. How high is the building and what is the maximum height of the tennis ball?
hf=hi+vi*t-4.9t^2
so you know hf(=0), vi, time t, solve for hi. Looks straightforward to me.
V = Vo + g*Tr = 0.
22 - 9.8Tr = 0.
Tr = 2.24 s. = Rise time.
Tr+Tf = 6.4.
2.24 + Tf = 6.4
Tf = 4.16 s. = Fall time.
h = 0.5g*Tf^2 = 4.9*4.16^2^2 = 84.8 m. above gnd. = ht. of tennis ball.
h = ho + Vo*Tr + 0.5g*Tr^2 = 84.8 m.
ho + 22*2.24 - 4.9*(2.24)^2 = 84.8.
ho + 24.69 = 84.8
ho = 60.1 m. = Ht. of the bldg.
To solve this problem, we can use the equations of motion to find the height of the building and the maximum height of the tennis ball.
Let's start with finding the height of the building.
We'll use the equation:
h = ut + (1/2) * g * t^2
where:
h = height
u = initial velocity (velocity when the ball is first thrown)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken to reach the ground
Given:
u = 22 m/s
t = 6.4 s
g = 9.8 m/s^2
Substituting the values into the equation, we get:
h = (22 * 6.4) + (0.5 * 9.8 * (6.4)^2)
Simplifying the equation:
h = 140.8 + 200.384
h = 341.184
Therefore, the height of the building is approximately 341.184 meters.
Next, let's find the maximum height of the tennis ball.
To find the maximum height, we can use the fact that the maximum height occurs when the vertical velocity of the ball is 0.
We'll use the equation:
v = u + gt
where:
v = final velocity (0 m/s at the maximum height)
u = initial velocity (22 m/s)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time to reach maximum height
Rearranging the equation to solve for the time (t), we have:
t = (v - u) / g
Substituting the values into the equation:
t = (0 - 22) / (-9.8)
Simplifying the equation:
t = -22 / -9.8
t = 2.2449 seconds (approximately)
Now that we know the time to reach the maximum height is approximately 2.2449 seconds, we can use this time and the equation for height (h) to find the maximum height.
Substituting the values into the equation:
h = (u * t) + (0.5 * g * t^2)
h = (22 * 2.2449) + (0.5 * 9.8 * (2.2449)^2)
Simplifying the equation:
h = 49.388 + 24.675
h = 74.063
Therefore, the maximum height of the tennis ball is approximately 74.063 meters.