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 = 19.6t and y = 3.88t ? 4.81t2, 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 = 3.24 s.
= m
= m/s
= m/s2

Explanation / Answer

a) x = 19.6t and y = 3.88t - 4.81t2

s(t) = 19.6t i + 3.88t - 4.81t^2 j

b)
V(t) = ds/dt = 19.6 i + (3.88- 9.62 t)j

c) a(t) = dv/dt = -9.62 j

d)

s(3.24) = 63.504 i - 88.41 j

v(3.24) = 19.6 i -27.28 j

a(3.24) = -9.62 j

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