A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as

Question

A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by

A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x = 19.3t and y = 3.72t ? 5.29t2, where x and y are in meters and t is in seconds. Write a vector expression for the ball's position as a function of time, using the unit v i^ and j^ . (Give the answer in terms of t.) By taking derivatives, do the following. (Give the answers in terms of t.) obtain the expression for the velocity vector v as a function of time obtain the expression for the acceleration vector a as a function of time Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.06 s.

Explanation / Answer

a) R = 19.3*t i + (3.72t -5.29t^2) j

b) V = dR/dt = 19.3 i + (3.72 - 10.58t) j

c) a = dV/dt = -10.58 j

d) at time t = 3.06 s

R = 19.3*t i + (3.72t -5.29t^2) j

R = 59.058 i - 38.15 j

V = 19.3 i - 28.655 j

a = -10.58 j

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