Question

A football player kicks a ball into the air with an initial velocity of 30 m/s at an angle of 60 degree relative to the ground.

What is the position of the football after 1 second along the x and y axis?




What is the velocity after 1 s?




What is its total time of flight?

Answer 1

Given:

$v_0=30\;\rm m/s$

$\theta=60^{\circ}$

The equations of motion of a ball

$$x(t)=v_0\cos\theta*t=30\cos 60^{\circ}*t=15t\\ y(t)=v_0\sin\theta*t-gt^2/2=26*t-4.9t^2$$

At the instant $t=1\:\rm s$

$$x(1)=15*1=15{\:\rm m}\\ y(1)=26*1-4.9*1^2=21\:\rm m$$

The velocity

$$v_x(t)=v_0\cos\theta=30\cos 60^{\circ}=15\:{\rm m/s}\\ v_y(t)=v_0\sin\theta-gt=26-9.8t$$

$$v_x(1)=15\:{\rm m/s}\\ v_y(1)=26-9.8*1=16\:\rm m/s$$

The total time of flight

$$t=\frac{2v_0\sin\theta}{g}=\frac{2*30\sin 60^{\circ}}{9.8}=5.3\:\rm s$$