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 = 17.8t and y = 4.36t ? 4.53t2, 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 i hat and j hat. (Give the answer in terms of t.) r with arrow = By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector v with arrow as a function of time v with arrow = (c) obtain the expression for the acceleration vector a with arrow as a function of time a with arrow = (d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 2.79 s. r with arrow = m v with arrow = m/s a with arrow = m/s2

Explanation / Answer

(a) r(t) = 20.0 m/s ti + (3.20m/s * t - 4.90 m/s/s*t^2) j
(b) v(t) = dr/dt = 20.0 m/s i + (3.20 m/s - 9.80 m/s/s t) j
(c) a(t) = dv/dt = 0 i - 9.80 m/s/s j = -9.80 m/s/s j
(d) r(4.40s) = 88.0 m (i) - 80.8 (j)

(f) v(4.40s) = 20.0 m/s (i) + (-39.9 m/s)(j)
(g) a(4.40s) = -9.80 m/s/s (j)

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