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
x = 16.6t
and
y = 4.36t ? 5.25t2,
where x and y are in meters and t is in seconds.

a/Write a vector expression for the ball's position as a function of time, using the unit vectors and . (Give the answer in terms of t.)
b/By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector as a function of time
c/(c) obtain the expression for the acceleration vector as a function of time

(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 2.88 s.
= m
= m/s
= m/s2

Explanation / Answer

a) position vector , r = 17.4t i + (3.92t - 5.21t2) j m Vx = dx/dt = 17.4 Vy = dy/dt = 3.92 - 10.42t Ax = dVx/dt = 0 Ay = dVy/dt = -10.42 b) velocity vector , v = 17.4 i + (3.92-10.42t) j m/s c) acceleration vector, a = -10.42 j m/s2 d) r = 17.4(2.88) i + (3.92(2.88) - 5.21(2.88)*(2.88)) j m = 50.1 i - 31.9 j m v = 17.4 i + (3.92 - 10.42 * 2.88) = 17.4 i - 26.1 j m/s a = -10.42 j m/s2

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