Answer:
Explanation:
A catapult launches a rocket at an angle of 53.0° above the horrizontal,
with an initial speed of 100m/s
The rocket engine immediately starts a burn, and for 3.00 s; the rocket moves allong its initial line of motion with an acceleration of 30.0 m/s²
Then its engine fails and the rocket proceeds to move in free fall.
(a) We are first to find the maximum altitude reached by the rocket:
Final velocity (v) = acceleration × time = 30m/s² × 3.00 s = 90 m/s
The initial velocity (u) is 100m/s
Average velocity = [tex]\frac{v + u}{2}[/tex] = [tex]\frac{90 + 100}{2}[/tex] = 95 m/s
Displacement = average velocity × time taken = 95m/s × 3.00 s = 285 m
(b) We are then to find total time of flight.
The initial velocity when the catapult is starting to fall is 90 m/s
The final velocity of the catapult = 0 m/s
Average velocity = [tex]\frac{v + u}{2}[/tex] = [tex]\frac{0 + 90}{2}[/tex] = 45 m/s
Time taken to fall = average velocity ÷ gravitational acceleration (9.8 m/s²) = 45 m/s ÷ 9.8 m/s² = 4.591836735 seconds = 4.59 s (to nearest two decimal places)
Total time taken = 3.00 s + 4.59 s = 7.59 s
