Question

The horizontal and vertical components of the initial velocity of a football are 20m/s and 30 m/s respectively. Assume that after rising some height, the football returns back to the ground level.

1) what is the speed of the football at 3s after launch?

2) to what maximum height does the football rise?

3)What horizontal distance does the football travel during its flight?

Please show full explaination and steps for answer.

Answer 1

Given initial velocity of football in vertical and horizontal directions are 30 and 20 m/s respectively

Football is motion with uniform acceleration in vertical direction and motion with uniform velocity in horizontal direction let acceleration due to gravity be 10 m/s^2 and is denoted by g

1

Equation of motion in vertical direction when body projected with initial velocity 'U'm/s and acceleration is 'g'm/s^2 in downward direction let velocity of body after t s be v m/s then

V=U-gt

So velocity of football after 3 s is v=[30]-[10].[3]=0

Therefore velocity of football after 3seconds is.ZERO in vertical direction

So speed of football is 20m/s as speed in horizontal direction is 20 and in vertical direction is zero

2

Maximum height reached by a body thrown vertically upwards with u m/s is u^2/2g

Therefore maximum height reached is 30^2/2(10)= 45m

Therefore maximum height reached is 45m

3

Time of flight of body thrown with u m/s is. 2u/g

Therefore time of flight is. 2 (30)/10=6s

So distance travelled in horizontal direction is 20(6)= 120 m As motion is with uniform velocity