a ball is thrown straight up with a speed of 8.0 m/s from a third-floor window located 13.0 m above ground. Calculate the maximum height, measured from the ground, of the ball; calculate the ball's velocity when it reaches the ground, and calculate the total time it takes the ball to reach the ground.
a. ho + (V-Vo^2)/2g=13 + (0-(8^2)/-19.6 = 16.3 m. Above gnd.
b. V^2 = Vo^2 + 2g*h
Vo = 0 m/s, 2g = 19.6 m/s^2, h = 16.3 m.
Calculate V.
c. V = Vo + g*Tr = 0.
Tr = -Vo/g = -8/-9.8 = 0.82 s=Rise time.
h = 0.5g*t^2 = 16.3 m.
4.9t^2 = 16.3
t^2 = 3.33
Tf = 1.82 s. = Fall time.
Tr+Tf = 0.82 + 1.82 = 2.64 s. = Total
time to reach gnd.
To find the maximum height, velocity at ground level, and the time taken by the ball to reach the ground, we can use the equations of motion. Here's how you can calculate each of these:
1. Maximum height (hmax):
The maximum height reached by the ball can be found using the equation:
hmax = (v^2 - u^2) / (2g)
where v is the final velocity (which is 0 m/s at the maximum height), u is the initial velocity (8.0 m/s), and g is the acceleration due to gravity (9.8 m/s^2).
Plugging in the values:
hmax = (0^2 - 8.0^2) / (2 * 9.8)
2. Velocity at ground level (vground):
The velocity at ground level can be found using the equation:
v = u + gt
where v is the final velocity (which is what we need to find), u is the initial velocity (8.0 m/s), g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken to reach the ground (what we also need to find).
We can rearrange the equation to solve for v:
v = u + gt
3. Total time taken (t):
The time taken to reach the ground can be found using another equation of motion:
h = ut + (1/2)gt^2
where h is the initial height (13.0 m), u is the initial velocity (8.0 m/s), g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken to reach the ground (what we need to find).
We can rearrange this equation to solve for t:
13.0 = 8.0t + (1/2) * 9.8 * t^2
By solving these equations, you can find the maximum height, velocity at ground level, and the total time taken by the ball to reach the ground.