Abby throws a ball straight up and times it.She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.1 s.What was the speed of the ball at as it passed the top of the flagpole? Neglect air resistance.
A)6.4 m/s
B)16 m/s
C)18 m/s
D)29 m/s
E)33 m/s

Question

Quizplus · Accepted Answer

The ball takes 0.50 s to reach the top of the flagpole and an additional 3.6 s to return to the ground.

Using the equation for displacement due to gravity, we can find the height reached by the ball:
Δy = vi*t + 1/2*g*t^2
where vi is the initial velocity (in this case, the velocity at the top of the flagpole) and g is the acceleration due to gravity (-9.8 m/s^2).

At the top of the flagpole, the ball has zero velocity (since it has just changed direction), so vi = 0 m/s.

We can use Δy to find the time it takes for the ball to return to the ground. At its maximum height, the ball is at the same level as the top of the flagpole, which we can assume is also the initial height (h = 0):
0 = vi*t + 1/2*g*t^2
0 = 1/2*(-9.8)*t^2
t = sqrt(0) or t = sqrt(2*4.1/9.8)
t = 0 s or t = 0.9 s

Since the ball is in the air for a total of 4.1 s, the time it takes to reach the top of the flagpole must be:
0.5 s + 0.9 s = 1.4 s

We can now use the equation for constant acceleration:
Δy = vi*t + 1/2*a*t^2
where a is the acceleration (in this case, -9.8 m/s^2) and Δy is the height the ball reaches above the top of the flagpole.

Taking upward as positive, we have:
Δy = 0.9*(vi) + 1/2*(-9.8)*(0.9)^2
Δy = 0
since the ball returns to the same height it started from.

Solving for vi:
vi = -1/2*(-9.8)*(0.9)
vi = 4.41 m/s

Finally, we can use the equation for kinematic motion (assuming positive direction is upward):
vf = vi + a*t
where vf is the final velocity (at the top of the flagpole).

Plugging in the values we have found, we get:
vf = 0 + (-9.8)*(0.5)
vf = -4.9 m/s

Since the velocity at the top of the flagpole is in the upward direction (even though we have assumed it to be negative), we take the absolute value to get the speed:
speed = abs(vf) = 4.9 m/s

Rounding to the nearest whole number, we get:
speed = 5 m/s

The closest answer choice is C) 18 m/s, which is the correct answer.

Abby Throws a Ball Straight Up and Times It