# A medieval prince trapped in a castle wraps a message around a rock and throws it from the top of the castle with an initial velocity of 12m/s[42 degrees of above the horizontal]. The rock lands just on the far side of the castle's moat, at a level 9.5m below the initial level. Determine the rock's time of flight. ...?

Vertical acceleration = - g
Vertical velocity = u sinѲ - gt [Ѳ = 42; u = 12 m/s]
Vertical displacement = u sinѲt - (1/2) g t^2 + 9.5

When the rock hits the ground, its vertical displacement will be zero. So we can say..

u sinѲt - (1/2) g t^2 + 9.5 = 0
I'll rearrange this ....

- (1/2) g t^2 + u sinѲt + 9.5 = 0

Can you see that we now have a quadratic in t?

Using the well known formula

t = [ - u sinѲ ± √( u^2 sin^2Ѳ - 4(( - (1/2)g * 9.5))] / (- g)

t = [- u sinѲ ± √( u^2 sin^2Ѳ + 19g)] / (-g)

t = [- 8.03 ± √(250.86)] / (-9.81)

t = [- 8.03 ± 15.84] / (-9.81)

t = (- 8.03 + 15.84) / (-9.81) or t = (-8.03 - 15.84) / (-9.81)

t = - 0.8 or t = 2.43

Well, a negative time has no meaning so
t = 2.43 seconds.

## Related Questions

What is concave mirror​

A curved mirror is a mirror with a curved reflecting surface. The surface may be either convex or concave. Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices.

Explanation:

Should the antireflection coating of a microscope objective lens designed for use with ultraviolet light be thinner, thicker, or the same thickness as the coating on a lens designed for visible light?

the thickness to meet the equation must be less than in a system for visible Liz                      t _UV < t_visible

Explanation:

When a ray enters the film antireflector that generally has a refractive index greater than the glass index, it experiences a phase change of 180, similar to when we have a collision with a wall.

When the beam reaches the bottom of the film-glass interface film, the refractive impact of the film is greater than that of the glass, it does not experience any change in phase.

Within the film the beam experiences a change in its propagation speed, the frequency in the air and the film is the same, since the propagation of a resonant type process, to fulfill the equation

v = λₙ f

The wavelength must change c = λ₀ f

c / v = λ₀ /λₙ

n = λ₀ /λₙ

λₙ = λ₀ / n

In general this type of reflection is almost normal to the surface, so we can calculate the optical path difference, if t is the thickness of the film, for constructive interference

2t = m λₙ  + λₙ / 2

2t = (m + ½)  λₙ

This is the condition to see a bright beam.], For destructive interference the equation is

2t = m λₙ

t = m λₙ / 2

Since the wavelength of visible light 400 to 700 is not much male than the wavelength of ultra violet light Lam

Give a specific example of a machine,and describe how its mechanical efficiency might be calculated