(a) What are the coordinates of the initial position of the stone? Xo= 0m Yo= 66

Question

(a) What are the coordinates of the initial position of the stone?

Xo= 0m

Yo= 66m

(b) What are the components of the initial velocity?

Vox= 15 m/s

Voy= 0 m/s

(c) Write the equations for thex- andy-components of the velocity of the stone with time. (Use the following as necessary:t. Let the variabletbe measured in seconds. Do not state units in your answer.)

Vx=

Vy=

(d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary:t. Let the variabletbe measured in seconds. Do not state units in your answer.)

x=

y=

Explanation / Answer

In this case (or almost all projectile motion problems), you can decompose the motion of the ball into vertical and horizontal motion. They can be considered as completely separate. A) Using the formula: s = (1/2)at^2 rearrange: t = squareroot(2s/a) = squareroot (2*53/9.8) = 3.3 seconds B) The 21m/s in the horizontal direction remains constant. Calculate the vertical speed when it hits the bottom. v^2 = u^2 + 2as v = squareroot(u^2 + 2as) = squareroot (0 + 2*9.8*53) = 32.2m/s The 2 velocities will have to be added vectorially. The speed is = squareroot(32.2^2 + 21^2) = 38.5m/s angle = arctan (32/21) = 56.6degrees above horizontal

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