Question

A particle is projected horizontally with a speed 5m/s from the top of a plane inclined at an angle theta=37 to the horizontal as shown in figure : Find the time taken by the particle to hit the plane. {Take g=10m/s}

Answer 1

A particle is projected horizontally with a speed 5m/s from the top of a plane inclined at an angle, θ = 37° to the horizontal as shown in figure.

To find : The time taken by the particle to hit the plane.

here component of acceleration perpendicular to plane, $a_x=gcos\theta$

component of initial velocity perpendicular to plane, $u_x=usin\theta$

now using formula, $x=u_xt+\frac{1}{2}a_xt^2$

for t = T(time of flight) , x = 0

so, 0 = usinθ T - 1/2 gcosθ T²

⇒T = 2usinθ/gcosθ using this formula we can get time.

here θ = 37° , u = 5 m/s and g = 10 m/s²

so, T = (2 × 5 × sin37°)/(10 cos37°)

= 3/4 s

Therefore the time taken by the particle to hit the plane is 3/4 sec