question on projectile physics

Question

A stone is projected from a point O on a cliff with a speed of 20m/s at an angle of elevation of 30 degrees. T seconds later the angle of depression of the stone from O is 45 degrees. find the value of T

Answer 1

PROBLEM

 

question on projectile physics
A stone is projected from a point O on a cliff with a speed of 20m/s at an angle of elevation of 30 degrees. T seconds later the angle of depression of the stone from O is 45 degrees. find the value of T

 

SOLUTION

 

Diagram:

 

           20 m/s

            /

_____O/30° - - - - - - - - - -                         

******                               \45°

******                                \

******

 

Equations for projectile motion:

 

v = v₀ + at

 

x = x₀ + v₀t + (1/2)at²

 

v_0x = v₀cosθ

 

v_0y = v₀sinθ

 

v_0x = v₀cosθ = 20cos30° = 20√3

 

v_0y = v₀sinθ = 20sin30° = 20(1/2) = 10

 

Since, v_x = v_0x throughout the flight of the stone, when the stone is at an angle of depression = 45°, v_x = -v_y = 20√3

 

v_y = v_oy + at

 

-20√3 = 10 - 9.8t

 

-20√3 - 10 = -9.8t

 

[-20√3 - 10]/(-9.8) = t

 

t = 4.55520573 s

 

t ≈ 4.6 s