speed v_0 at an angle 0 above the horizontal. This planet is a strange one, in t

Question

speed v_0 at an angle 0 above the horizontal. This planet is a strange one, in t lat the acceleration due to gravity increases linearly with time starting with a value of zero when the projectile is fired. In other words, g(t) = beta t, where beta is a given constant. What horizontal distance does the projectile travel? What should & be to maximize this distance? Newton is tired of apples falling on his head, so he decides to throw a rock at one of the larger and more formidable-looking apples positioned directly above his favorite sitting spot. Forgetting all about his work on gravitation, he aims the rock directly at the apple (see Fig. 3.28). To his surprise, the apple tails from the tree just as he releases the rock. Show, by calculating the rock s height when it reaches the horizontal position of the apple, that the rock hits the apple. Two balls are fired from ground level, a distance d apart fired vertically with speed v (see Fig. 3.29). You wish to s This problem suggests a wav in which William Tell and his son might survive

Explanation / Answer

let H be the height of the apple

let Vo be the velocity with which newton throws the stone towards the apple.

let x be the height at which stone hits the apple.

let t be the time after which the apple is hit by the stone,.

so displacement of stone

x = Vot -(1/2)gt2

displacement of apple

H-x = (1/.2)gt2

adding both the equations we get

H = Vot

t = H/Vo

putting the value of t

we get

x = Vo(H/V0) -(1/2)g(H/V0)2

x = H - (1/2)g(H/Vo)2

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