A stone is projected from the ground with velocity 50 ms−1 and angle of 30∘. It crosses a wall after 3 s. How far beyond the wall the stone will strike the ground?

To solve this problem, we need to break it down into several steps:

Step 1: Calculate the initial horizontal and vertical velocities. The initial velocity (u) is given as 50 m/s and the angle (θ) is 30 degrees. We can find the initial horizontal velocity (u_x) and the initial vertical velocity (u_y) using the equations:

u_x = u * cos(θ) = 50 * cos(30) = 43.3 m/s u_y = u * sin(θ) = 50 * sin(30) = 25 m/s

Step 2: Calculate the time it takes for the stone to hit the ground. The stone crosses the wall after 3 seconds, but we need to find out when it hits the ground. We can use the equation of motion:

h = u_y * t - 0.5 * g * t^2

where h is the height (which is 0 when the stone hits the ground), g is the acceleration due to gravity (9.8 m/s^2), and t is the time. Solving for t gives us:

0 = 25 * t - 0.5 * 9.8 * t^2 0 = t * (25 - 4.9 * t)

This equation has two solutions: t = 0 (at the start) and t = 25 / 4.9 = 5.1 seconds (when the stone hits the ground).

Step 3: Calculate the horizontal distance travelled by the stone. The horizontal distance (d) travelled by the stone is given by the equation:

d = u_x * t

Substituting the values we have:

d = 43.3 * 5.1 = 221 m

Step 4: Calculate the distance beyond the wall where the stone will strike the ground. The stone crosses the wall after 3 seconds, so the distance to the wall is:

d_wall = u_x * 3 = 43.3 * 3 = 130 m

So, the distance beyond the wall where the stone will strike the ground is:

d - d_wall = 221 - 130 = 91 m

So, the stone will strike the ground 91 m beyond the wall.