Question

A rocket is launched from rest and moves in a straight line at 65.0 degrees angle above the horizontal with an acceleration of 42.0m/s square. After 32.0 s of powered flight, the engines shut off and the rocket follows a parabolic path back to Earth. Find the time of flight from launching to impact. What is the maximum altitude reached? What is the distance from launch pad to impactpoint? Ignore the variation in g with height

Answer 1

First we have to calculate the velocity of rocket after the powered flight.

which is

distance travelled during this duration.

Now we can calculate horizontal and vertical distance of rocket from the launch pad

Horizontal = s*Cos65

Vertical = s*Sin65

Similarly we can calculate the horizontal and vertical component of velocity as

Time to reach the highest point when verical velocity become zero

and distance travelled in vertical direction during this is

and time to reach the the rocket to ground can be calculated by

Total distance travelled = 75690 + 19490 =95180 m

Total time of flight is the sum of all three times as

So the total time of flight is 295.7 s

To calculate the maximum altitude reached we have to add two distances

To calculate the horizontal distance we have to calculate the distance travelled in time t1 and t2 in x direction

So the horizontal distance from the impact point is equal to 158870 m