A catapult on a cliff launches a large round rock towards a ship on the ocean below. The rock leaves the catapult from a height H = 31.0 m above sea level, directed at an angle theta = 49.3° above the horizontal, and with a speed v = 30.7 m/s. Assuming that air friction can be neglected, calculate the horizontal distance D traveled by the projectile.
-
first figure out the velocity in the x and y direction. Hint: make a triangle, the hypotenuse is the 30.7m/s and the angle is the 49.3.
Next find out how long it will take for the rock to go from 31m to sea level, that will give you time Hint: find an equation with time, acceleration, distance and velocity. Preferably one that only has one time variable, not one that has time squared. acceleration is just gravity and velocity is the y value you got in the first step.
Finally take the x value you got from the triangle and the time value you got from the last step and put them into an equation for distance. Hint: acceleration in the x direction is zero. make sure to use an equation that has time elsewhere besides attached to the acceleration (as in velocity and time together as part of the equation)
That should give you your answer. I would have posted the equations but I'm really tired and just about to head to bed and the equations are getting all jumbled up... so I didn't want to give you a wrong equation.
Next find out how long it will take for the rock to go from 31m to sea level, that will give you time Hint: find an equation with time, acceleration, distance and velocity. Preferably one that only has one time variable, not one that has time squared. acceleration is just gravity and velocity is the y value you got in the first step.
Finally take the x value you got from the triangle and the time value you got from the last step and put them into an equation for distance. Hint: acceleration in the x direction is zero. make sure to use an equation that has time elsewhere besides attached to the acceleration (as in velocity and time together as part of the equation)
That should give you your answer. I would have posted the equations but I'm really tired and just about to head to bed and the equations are getting all jumbled up... so I didn't want to give you a wrong equation.