Calculating a Prince's Message: Flight Time, Moat Width and Impact Velocity

[LampMan]

Homework Statement

A prince trapped in a castle wraps a message around a rock and throws it from the top wall with an initial velocity of 12 m/s [42 deg above the horizontal] the rock lands just on the far side of the castles moat at a level 9.5m below the initial level. determine the rocks:
a) time of flight
b) width of moat
c) velocity of impact

Homework Equations

i don't know I've lost my formula sheet (but theyre basic ones) if i can just have my memory refreshed on what the equations are i can probably do it plus be able to continue on the rest of the unit exam review. my exam is next week and this question isn't for marks but for studying and i need help please

The Attempt at a Solution

dont know where to start

 

[payumooli]

v = u + a*t
s = ut + 0.5*a*t^2
v^2 = u^2 + 2as

v - final velocity
u - initial velocity
s - distance traversed

use the two components of the initial velocity and proceed

 

[kerimek]

I would first gather all the relevant information from the given scenario. From the initial velocity (12 m/s at 42 degrees above horizontal), I can calculate the initial horizontal and vertical components of the velocity using the equations v_x = v*cos(theta) and v_y = v*sin(theta). In this case, v_x = 12*cos(42) = 8.59 m/s and v_y = 12*sin(42) = 7.93 m/s.

Next, I would use the equation y = y_0 + v_y*t - 0.5*g*t^2 to calculate the time of flight (t) by setting y = 9.5 m (final height) and y_0 = 0 (initial height). Solving for t, I get t = 1.62 seconds.

To calculate the width of the moat, I would use the equation x = x_0 + v_x*t, where x_0 is the initial horizontal position (which we can assume to be 0 since the rock is thrown from the top of the wall). Plugging in the values, I get x = 8.59*1.62 = 13.92 meters. Therefore, the width of the moat is approximately 13.92 meters.

Finally, to calculate the velocity of impact, I would use the equation v^2 = v_x^2 + v_y^2 - 2*g*(y - y_0) where v is the total velocity at impact and y is the final height (9.5 m) and y_0 is the initial height (0). Solving for v, I get v = 12.07 m/s.

In conclusion, the time of flight is 1.62 seconds, the width of the moat is approximately 13.92 meters, and the velocity of impact is 12.07 m/s. These calculations can help the prince determine the best way to get his message across the moat to reach potential rescuers.