A catapult launches a rocket at an angle of 50.3° above the horizontal with an i

Question

A catapult launches a rocket at an angle of 50.3° above the horizontal with an initial speed of 104 m/s. The rocket engine immediately starts a burn, and for 3.11 s the rocket moves along its initial line of motion with an acceleration of 24.7 m/s2. Then its engine fails, and the rocket proceeds to move in free-fall.

A catapult launches a rocket at an angle of 50.3 above the horizontal with an initial speed of 104 m/s. The rocket engine immediately starts a burn and for 3.11 s the rocket moves along its initial line of motion with an acceleration of 24.7 m/s2. Then its engine fails, and the rocket proceeds to move in free-fall. (a) Find the maximum altitude reached by the rocket. (b) Find its total time of flight. (c) Find its horizontal range. m

Explanation / Answer

till 3.11 sec

distance travelled=104*3.11 +(0.5*24.7*3.11^2)=442.89 m

height=442.89sin(50.3)=340.75

horizontal distance=442.89cos(50.3)=282.9 m

velocity=104+24.7*3.11=180.817 m/s

vertical component at that height=180.817sin(50.3)=139.12 m/s

horizontal component=180.817cos(50.3)=115.5 m/s

time taken to come to rest=139.12/9.8=14.2 sec

more height travelled=139.12*14.2-0.5*9.8*14.2^2=986.9

maximum altitude=986.9+340.75=1327.65 m

(b) time of flight=14.2+3.11=17.31 sec

(c) range=282.9+(14.2*115.5)=1923 m

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