Question

A football kicked off at an angle 20° from the ground reaches a maximum height of 4.7 m. What is the initial velocity of the kick?

28m/s
18m/s
15m/s
11m/s

Answer 1

To solve this problem, you need to consider what magnitude the vertical component of the velocity would need to be to reach the maximum height. Then it will just be simple trigonometry to find the total velocity.

Answer 2

I'm not sure what you mean.. Could you explain that? @Pompeii00

Answer 3

Surely. Sorry for the delay.

So we know the football will only reach 4.7 m. This means that the vertical component of the velocity (which will decrease over time as gravity acts and impedes the motion) will be 0 at the max height.

So we need to find a speed, which when decreased over time, stops at a height of 4.7 m.

I'm sure you've been introduced to kinematic equations. I would suggest the equation that does not depend on time directly:

Vf^2 = Vi^2 + 2*A*X

A = g = -9.8 m/s^2
X = 4.7 m
Vf = 0 m/s
Vi = ? <-- this is what we're looking for here

0 = Vi^2 - 2 * 9.8 * 4.7

If you solve this, you should find Vi = 9.6 m/s

So this is the vertical velocity we start with initially. Now we will use trigonometry to solve for the total velocity.


So the initial velocity at 20 degrees inclination is 28.1 m/s. This agrees with the first answer option of 28 m/s.

Answer 4

I got 10.54, so appox 11 :/