# What is the time of flight, maximum altitude and horizontal range of a rocket launched at an angle of θ = 55° to the horizontal with an initial speed v = 66 m/s.

justaguide | College Teacher | (Level 2) Distinguished Educator

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The rocket is launched with an initial velocity of 66 m/s in a direction making an angle of 55 degree to the horizontal.

The rocket's velocity can be divided into the horizontal and vertical components. The vertical component is 66*sin 55 and the horizontal component is 66*cos 55.

As the rocket moves there is a downward acceleration of 9.8 m/s^2. This reduces the vertical velocity and it reaches 0 at the highest point. Let the time taken by the velocity to reach 0 be t.

66*sin 55 - 9.8t = 0

=> t = 66*sin 55/9.8 = 5.51 s

The time of flight is 2*v*sin x/g = 11 sec.

For half this duration the rocket is moving upwards. The maximum altitude is 66*sin 55*5.51 = 594.7 m.

The maximum horizontal distance is 66*cos 55*11= 416 m

The time of flight of the rocket is 11 s, the maximum altitude is 149 m and the horizontal range is 416 m.