Question

A player kicks a football at an angle of 30.0 above the horizontal. The football has an initial velocity of 20.0 m/s. Find the horizontal component of the velocity and the maximum height attained by the football.
a. 10.0 m/s, 17.6 m
b. 17.3 m/s, 5.10 m
c. 25.1 m/s, 7.40 m
d. 30.3 m/s, 9.50 m ido

Answer 1

Answer:

Option b) 17.3 m/s and 5.10 m

Explanation:

For this case, we can consider a parabolic shot, for which we have an initial speed of 20 m/s, which has a vertical component (Voy) and a horizontal component (Vox)  - see attached picture 1 on this case -

According to the figure, we have a right rectangle, for which we can obtain the following formulas:

V₀ₓ= V₀Cosα

V₀y=V₀Senα

With these formulas, we can first obtain the horizontal component of velocity:

V₀x=20xCos30= 17.32 m/s

Then we need to obtain the maximum height (point C on the chart). At this point, we can think about a freefall, where speed is given by :

V=gt , where g= gravity acceleration  and t=time

Our maximun time at point C will be: tmax=V/t, and we can replace vertical component of speed, given by V₀Senα, then:

Tmax=V₀Senα/g

Finally, if we still consider a movement in free fall, time is given by :

t= √(2h/g)   then h=(gt²)/2 and replacing our time previously found:

hmax=(V₀xsenα)²/2g

And replacing our numbers: hmax= 5.10 m