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 = 17.1t
and
y = 4.40t ? 4.73t2,
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.)
=

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) 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 = 2.82 s.
= m
= m/s
= m/s2

Explanation / Answer

The horizontal motion of the ball is at cosntant speed using equation of x = Vx*t Given x = 16.6*t We conclude that Vx = 18 m/s Comparing the given y(t) equation of y(t) = 4.36* - 4.25*t^2 with the equation of free fall of h(t) = h0 + Vy*t + (1/2)*g*t^2 We see that h0=0 Vy=4.5 m/s (Vy>0) a=-4.9 (a

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