You accidentally throw your car keys horizontally at 8.0 m/s from a cliff. If yours keys land 28 m from the base of the cliff, how high was the cliff? Question 10 options: 17.15 m 60 m 45 m 28 m

Explanation:

Let be the horizontal speed of the keys and D be the horizontal distance covered by the keys.

The initial velocity in the vertical direction is .

Let be the acceleration due to gravity, which always acts vertically downwards, so, it will not change the horizontal direction of the speed, i.e. will remain constant throughout the projectile motion.

Let be the total time of flight in seconds. So,

Let be the hight of the cliff.

Now, from the equation of motion

Where is the displacement is the direction of force, is the initial velocity in the direction of force,   is the constant acceleration due to force and is the time of flight.

Here, , and  (negative sign is for taking the sigh convention positive in the direction as shown in the figure.)

From equation (ii)

Take and put the value of from equation (i), we have

.

Hence, the height of the cliff was .

grav potential energy