A test rocket starting from rest at point A is launched by accelerating it along

Question

A test rocket starting from rest at point A is launched by accelerating it along a 200 0-m incline at 1.30 m/s^2 (Figure 1). The incline rises at 35.0 degree above the horizontal, and at the instant the rocket leaves it, its engines turn off and the rocket is subject to gravity only (ignore air resistance). Find the maximum height above the ground that the rocket reaches. Express your answer with the appropriate units. Find the rocket's greatest horizontal range beyond point A. Express your answer with the appropriate units.

Explanation / Answer

On incline :

Applying vf^2 - vi^2 = 2 a d

v^2 - 0^2 = 2(1.30)(200)

v = 22.8 m/s

after that it will be on free fall.

ay = 9.8 m/s^2

initial vertical velocity. v0y = 22.8 sin35 = 13.1m/s

Applying vf^2 - vi^2 = 2 a d

0^2 - 13.1^2 = 2 (-9.8)(h)

h = 8.73 m

maximum height = h + 200 sin35 = 123.4 m ........Ans

(B) as it leaves the plane:

h = 200 sin35 = 114.7 m

Applying y = v0 t + a t^2 / 2

0 - 114.7 = (13.1) t + (-9.8 t^2) /2

4.9 t^2 - 13.1 t -114.7 =0

t = 6.36 sec

horizontal distance travelled = (22.8 cos35) (6.36)

= 118.8 m

horizontal range = 118.8 + (200 cos35)

= 282.6 m ...........Ans

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