A projectile is fire straight upward at a speed of 50m/s from edge... (PRETTY SIMPLE PHYSICS HELP)?

Question

A projectile is fire straight upward at a speed of 50m/s from edge of a cliff 20m above a river. It just misses the cliff on the way down. With what speed does it land in the river?

A little explanation please. New to physics, so be nice :)

Answer 1

Consider upward direction as positive.

Initial velocity u = 50 m/s

The projectile falls 20 m below the cliff.

Therefore, displacement s = -20 m (negative because upward direction is taken as positive and the displacement is in downward direction)

Acceleration a = -g = -9.8 m/s^2 (negative because acceleration due to gravity is in downward direction)

Final velocity v = ?

v^2 = u^2 + 2as

Or, v^2 = 50^2 + 2 * (-9.8) * (-20)

= 2500 + 292

= 2892

Or, v = sqrt(2892) m/s = 53.78 m/s

Ans: 53.78 m/s

Answer 2

In simple terms, the solution to this problem can be determined in two steps.

First step is to determine the maximum height that the projectile will attain with respect to the edge of the cliff.

The working formula is

Vf^2 - Vo^2 = 2gs

where

Vf = final velocity = 0 (when body is at its maximum height)

Vo = 50 m/sec (given)

g = acceleration due to gravity = 9.8 m/sec^2

s = maximum height attained by body

Substituting appropriate values,

0 - 50^2 = 2(-9.8)(s)

NOTE the negative sign attached to the acceleration due to gravity. This simply denotes that the projectile is slowing down as it is going up.

Solving for "s",

s = 2500/(2 * 9.8)

s = 127.55 meters

Step 2 is to determine the speed at which the projectile lands in the river. The working formula is still

Vf^2 - Vo^2 = 2gs

but this time,

Vf = final velocity = velocity at which body will hit the water

Vo = initial velocity = 0 (at its maximum height, velocity = 0)

g = 9.8 m/sec^2

S = 20 + 127.55 = 147.55

Substituting appropriate values,

Vf^2 - 0 = 2(9.8)(147.55)

Solving for Vf,

Vf = 53.79 m/sec

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Using the same formula above, another way of solving this problem is to substitute the following numbers as in,

Vf^2 - Vo^2 = 2as

Vf^2 - (50)^2 = 2(9.8)(20)

I trust that you can solve for Vf from the above.