(14%) Problem 1: A ball is kicked at ground level with an initial velocity of 19

Question

(14%) Problem 1: A ball is kicked at ground level with an initial velocity of 19.5 m/s in the horizontal direction and 12.5 m/s in the vertical direction 33% Part (a) At what speed does the ball hit the ground in m/s? Grade Summary Deductions Potential 10 sinO cotan atan) acotanO s cosh)tanhO cos0) tanO Jt( acos) sinhO Submissions Attempts remaining (1%per attempt) detailed view sin cotnhO 0 Degrees O Radians 0 Submit Hint I give up! Hints: 0% deduction per hint. Hints remaining: 5 Feedback: 0% deduction per feedback 33% Part (b) For how long does the ball remain in the air in seconds? 33% Part (c) What maximum height is attained by the ball in meters?

Explanation / Answer

vox = initial velocity in horizontal direction = 12.5 m/s

voy = initial velocity in vertical direction = 19.5 m/s

net initial velocity is given as

vo = sqrt(vox2 + voy2) = sqrt((12.5)2 + (19.5)2) = 23.2 m/s

Using conservation of energy

final kinetic energy of ball before hitting the ground = initial kinetic energy of ball just after hitting

(0.5) m vf2 = (0.5) m vo2

vf = vo

vf = 23.2 m/s

b)

consider the motion along the Y-direction

voy = initial velocity = 19.5 m/s

y = displacement = 0 m

a = acceleration = - 9.8 m/s2

t = time taken

Using the equation

y = voy t + (0.5) a t2

0 = 19.5 t + (0.5) (- 9.8) t2

t = 4 sec

c)

consider the motion of ball from initial point of launch to maximum height along Y-direction

Ymax = maximum height gained

vfy = final velocity at the maximum height = 0 m/s

voy = initial velocity = 19.5 m/s

a = acceleration = - 9.8 m/s2

using the equation

vfy2 = voy2 + 2 a Ymax

02 = 19.52 + 2 (- 9.8) Ymax

Ymax = 19.4 m

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