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1)A)Suppose that Arpod hits a baseball so that it leaves his bat at a speed of v

ID: 1328302 • Letter: 1

Question

1)A)Suppose that Arpod hits a baseball so that it leaves his bat at a speed of v0 feet per second at an angle of 25o towards the outfield wall. Find the position vector, r(t), that gives the position of the ball at time t. Assume he hit the ball three feet above the ground. (Your answer will depend on v0) Also, assume that the only force acting on the ball in flight is the force due to gravity, and use g = 32 ft/sec2.

2)B)Will the ball clear the outfield wall if v0 = 110 feet per second (75 miles per hour)? To answer this, assume the outfield fence is 10 feet high and 350 from home plate.

3)D)What is the minimum value of v0 that will ensure that Arpod hits a home run? In case you’re not a baseball fan, that means the ball goes over the wall…

Explanation / Answer


intial velocity = vo

along horizantal = vox = vo*cos25

distance along horizantal = x = vox*t


x = vo*cos25*t ......(1)


along verticla voy = vo*sin25


distance along vertical y = voy*t + 0.5*g*t^2

y = vo*sin25*t + 0.5*g*t^2........(2)

position vector r = xi + yj

r = vo*cos25t i + ( voy*t + 0.5*g*t^2 ) j

2)

combinig 1 & 2

y = tan25*x - 0.5*g*x^2/(vo^2*(cos25)^2)


x = 350

y = 10 feet


g = 32 ft/s^2


10 = tan25*350 - 16*350^2/(vo^2*(cos25)^2)

vo = 125 ft/ s

the minimum speed required = 125 ft/s

the ball will not cross the wall

3)

Vmin = 125 ft/s