Question

A particle P is projected from a point A at the top of a cliff, 52 m vertically above sea level. It moves freely under gravity until it strikes the sea at a point S. The initial velocity components are 24 ms-1 horizontally and 7 ms-1 vertically.

The time of flight of the particle is

seconds

The horizontal distance AS is

m

The speed of the particle when it hits the sea is

s-1.

Answer 1

The physics question asks for the time of flight, horizontal distance, and impact speed of a projectile which are determined by the initial velocity components and the height of the cliff. A kinematic equation is used to solve for the time of flight, and subsequent calculations give the horizontal distance and impact speed.

Step-by-step explanation:

The time of flight for a projectile is determined by its vertical motion. In the given problem, we need to calculate the time of flight, horizontal distance, and the speed of the particle when it hits the sea.

To find the time of flight for particle P with an initial vertical velocity component of 7 m/s and descending 52 m, we use the kinematic equation for vertical motion under gravity (g = 9.81 m/s2) which is:

s = ut + 0.5gt2

Here, s is -52 m (negative because the particle is moving downwards), u is 7 m/s (initial vertical velocity), and g is 9.81 m/s2 (acceleration due to gravity). By substituting these values and solving the quadratic equation, we get the time of flight.

The horizontal distance AS can be found by multiplying the horizontal velocity component (24 m/s) by the time of flight since there is no horizontal acceleration.

The speed of the particle when it hits the sea is found by combining the final horizontal and vertical velocities (vx and vy) at the point of impact. The horizontal velocity remains constant at 24 m/s, and the final vertical velocity can be calculated using the equation vy = u + gt. These velocities are then combined using the Pythagorean theorem to find the total velocity (v).