A stone is catapulted at time t = 0, with an initial velocity of magnitude 19.5

Question

A stone is catapulted at time t = 0, with an initial velocity of magnitude 19.5 m/s and at an angle of 44.3 degree above the horizontal. What are the magnitudes of the (a) horizontal and (b) vertical components of its displacement from the catapult site at t = 1.15 s? Repeat for the (c) horizontal and (d) vertical components at t = 1.79 s, and for the (e) horizontal and (f) vertical components at t = 5.44 s. Assume that the catapult is positioned on a plain horizontal ground. (a) Number __________ Units (b) Number __________ Units (c) Number __________ Units (d) Number __________ Units (e) Number __________ Units (f) Number __________ Units

Explanation / Answer

initial velocity in horizontal, v0x = 19.5 cos44.3 = 13.96 m/s

in vertical direction, v0y = 19.5 sin44.3 = 13.62 m/s

acceleration in horizontal, ax = 0

in vertical, ay = - 9.81 m/s^2

and displacement, d = v0 t + a t^2 / 2

(A) Dx = (13.96 x 1.15) + 0 = 16.05 m

(B) Dy = (13.62 x 1.15) + (-9.81 x 1.15^2 / 2) = 9.18 m

(C) Dx = (13.96 x 1.79) = 25 m

(D) Dy = (13.62 x 1.79) + (-9.81 x 1.79^2 / 2) = 8.66 m

(E) Dx = 13.96 x 5.44 = 75.94 m

(F) Dy = (13.62 x 5.44) + (-9.81 x 5.44^2 / 2) = -71.06 m

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