Question

A soccer ball is kicked from the ground into The air with a velocity of 25 m/s at 45 degrees above horizontal. To the nearest meter, how high did the ball fly? How far did the ball travel before hitting the ground again assuming there was no wind resistance? (round to the nearest meter)

Answer 1

initial vertical speed=25*sin(45)=17.6776 m/s

at the highest point, vertical component will be 0.

acceleration due to gravity=-9.8 m/s^2

let maximum height be h.

then using the formula:

final speed^2-initial speed^2=2*acceleration*distance

==>0^2-17.6776^2=-2*9.8*h

==>h=15.9438 meters

hence to the nearest meter, it will fly to 16 meters of height.

part :

range of the projectile=v^2*sin(2*theta)/g

=25^2*sin(2*45)/9.8=63.7755 m

hence to the nearest meter, it will travel 64 meters before hitting ground again.