Robbie is playing baseball with his friends. He hits a pop fly that travels straight up in the air. The ball reaches a maximum height of 14.7 meters before falling back down...

Question

Robbie is playing baseball with his friends. He hits a pop fly that travels straight up in the air. The ball reaches a maximum height of 14.7 meters before falling back down toward the ground. How long will the ball remain in the air until it is caught by the catcher? (Assume the ball is caught at the same height that it is hit.)

Answer 1

Hi there!

We don't know when he catches the ball, but we'll work around that and you'll have to finish that part yourself. We're working with gravity and a maximum height, so let's use the following equation:

h = ½at² + v(0)*t + h(0) ; v(0) and h(0) are the initial velocity and height, respectively

Because the movement in this case is symmetrical - the distance and time traveled up are equal to the distance and time traveled down - we can work with half of the scenario, starting at the apex height.

a = g = - 9.8 m/s²

v(0) = 0 m/s ; the ball comes to a halt for an instant before descending.

h(0) = h_max = 14.7 m

h represents the height the ball reaches at time, t, but t is the goal here, so we will plug in a value for h and solve for t. The necessary information of catch height isn't shown here, but vaguely stated as "the height it is hit at," so let's just assume 1 m just to move forward - make sure to adjust appropriately to your case. Now we plug it all in and solve for t. We don't have an initial velocity, so we won't need to factor polynomials or use the quadratic formula.

1 m = ½ * -9.8 m/s² * t² + 14.7 m ; I'll simplify the ½ and gravity term and move the 1 m over

0 = -4.9 m/s² * t² + 13.7 m

-13.7 m = -4.9 m/s² * t²

-13.7 m / -4.9 m/s² = t² ; the negative values cancel

√ (13.7 m / 4.9 m/s²) = t

t = 1.672 s

The time it takes to fall from apex height is about 1.7 seconds, but this is only half the time it is in the air - it had to rise first! So, the answer is 2t:

2t = 2 * 1.672 s = 3.344 s

Keeping it vague for hit height, you will want to use:

_________________

2t = 2 √ ((h_max - h) / g) and solve for 2t.

Hope this helps, let me know if you have any questions!

Answer 2

2t = ? (s)

d 14.7

a = -g = -9.81m/s2

vf = 0

-vi = sqr rt of 2•(-9.81)•14.7 = 17m/s

since vf = vi + a•t

t = 1.73s therefore 2t = 3.46s

If you need further clarification or need one-on-one help, let me know.

Also visit my YouTube channel (Mr. A's Physics) for more solved problems.