Since the angle is 45˚, the vertical and horizontal components of the stone’s initial velocity are equal.

Vertical = 14 * sin 45

This is approximately 10 m/s.

During the time the stone is in the air, its vertical velocity decreases at the rate of 9.8 m/s each second. Let’s use the following equation to determine the stone’s vertical velocity as it strikes the water.

vf^2 = vi^2 + 2 * a * d

a = -9.8, d is the stone’s vertical displacement.

d = final height – initial height = 0 – 20 = -20 meters

vf^2 = (14 * sin 45)^2 + 2 * -9.8 * -20

vf^2 = 490

vf = ± √490

This is approximately 22.1 m/s. Since the stone is falling, its final vertical velocity is negative. . Let’s use the following equation to determine the total time the stone is in the air.

vf = vi – a * t

√490 = 14 * sin 45 – 9.8 * t

9.8 * t = √490 + 14 * sin 45

t = (√490 + 14 * sin 45) ÷ 9.8

The total time is approximately 3.3 seconds. During this time, the stone’s horizontal velocity is constant. Let’s use the following equation to determine the range.

d = v * cos θ * t

d = 14 * cos 45 * [(√490 + 14 * sin 45) ÷ 9.8

This is approximately 32.7meters.

b)At what velocity does the stone strike the water?

Final velocity = √(Final vertical velocity^2 + Final horizontal velocity^2)

Final velocity = √(490 + 98) = √588

This is approximately 24.2 m/s.

(14 * sin 45)^2 = 98

By using the following equation, you can determine the exact number for the stone’s final vertical velocity. Then use that number to determine the time. I think is easier than solving a quadratic equation.

vf^2 = vi^2 + 2 * a * d

I hope that this helps to understand how to solve this type of problem.

Vx = 14*cos(45) = 9.90 m/s

Vyi = 14*sin(45) = 9.90 m/s

Equation of motion

X = x0 + v0*t + 1/2*a*t^2

Horizontally:

x = vx*t

Vertically

y = hi + vyi*t - 1/2*g*t^2

From the horizontal

t = x/vx

Vertically, when the stone hits the water y = 0. Sub in t and solve for x

0 = hi + vyi*x/vx - 1/2*g*x^2/vx^2

0 = 20 + x - 0.050*x^2

Quadratic equation

X = 32.4 m .... ans A

Get the time

t = 3.3 s

Get the final vert velocity

Vyf= vyi - g*t = -22.4 m/s

Final velocity

V = sqrt(vx^2 + vyf^2) = 24.5 m/s