Show your work. Use correet numbers of significant figures and include your unit

Question

Show your work. Use correet numbers of significant figures and include your units (12 pts) A football is kicked from level ground. At its highest point, its speed is 15.0 m/s and the height is 10.0 m. 5 pts) Find the initial veloceity of the football. in unit vector notation Iculate the time of flight for the foothll, assuming in wi a t th ground and the ballod ko m sooif so, by how much The all cleare the enipt i aa ,If the horizontal bhar of the goalpost is 3,0s m above the away, wil the horizontal bar of the c 13 pts) If the horiaso goalpost

Explanation / Answer

a)

consider the motion along the vertical direction :

Voy = initial velocity

Vfy = final velocity at highest point = 0 m/s

a = acceleration = - 9.8 m/s2

Y = vertical displacement = 10 m

using the equation

Vfy2 = Voy2 + 2 a Y

02 = Voy2 + 2 (-9.8) (10)

Voy = 14 m/s

consider the motion along the horizontal direction :

Vox = initial velocity

Vfx = final velocity at highest point = 15 m/s

we know that since acceleration along the horizontal direction is zero , velocity along X-direction remains same

so Vox = Vfx = 15 m/s

In vector notation , initial velocity is then given as

Vo = Vox i + Voy j = 15 i + 14 j

b)

consider the motion along the Y-direction

t = time of flight = ?

Y = vertical displacement = 0 m

Voy = initial velocity = 14 m/s

a = acceleration = - 9.8 m/s2

using the equation

Y = Voy t + (0.5) a t2

0 = 14 t + (0.5) (-9.8) t2

t = 2.86 sec

c)

consider the motion along X-direction

t = time of travel

X = horizontal distance to be travelled to reach the goalpost = 35 m

Vox = velocity along horizontal direction = 15 m/s

time taken to reach goal post is given as

t = X/Vox = 35/15 = 2.33 sec

consider the motion along Y-direction

Y' = height of the ball at time "t"

using the equation

Y' = Voy t + (0.5) a t2

Y' = 14 (2.33) + (0.5) (-9.8) (2.33)2

Y' = 6.02 m

hence the ball clears the goalpost

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