Help:Projectile Motion - Solve Angle & Hill Height

[the_d]

**help:projectile Motion***

im giving a problem where i have to find the angle a projectile situated at the top of a will hit an boat wit constant velocity 20 ft/s 5 sec after starting at Vo = 96.6 ft/s and also how high the hill is above the water. The distance from the base of the hill to the boat is given to be 301 ft. Do i need to find the (Vo)x and (Vo)y with tan (-1) in order to get the angle and can i just assume the triangle to be a 3-4-5 triangle?

 

[Astronuc]

This is a homework problem and should be posted in the Homework section - Introductory Physics - would be appropriate.

One basically has to find the parabolic trajectory of the projectile and where it intersects the boat after the projectile and the boat both travel some distance during 5 seconds.

The distance from the base of the hill to the boat is given to be 301 ft.

It would appear that the boat starts 301 feet from the point even with the projectile. The horizontal velocity of the projectile must be such that it travels the initial distance from the boat + boat distance traveled by boat in 5 seconds.

 

[ravenprp]

To solve this problem, you will need to use the equations of projectile motion. First, you will need to find the initial horizontal and vertical velocities, (Vo)x and (Vo)y, using the given velocity and the angle at which the projectile is launched. You can use the inverse tangent function (tan^-1) to find the angle, but you will need to use the Pythagorean theorem to find the magnitude of the initial velocity.

Once you have (Vo)x and (Vo)y, you can use the equations of projectile motion to find the time it takes for the projectile to reach the boat, which is given to be 5 seconds. Then, you can use this time and the initial vertical velocity to find the height of the hill using the equation h = (Vo)y*t - 1/2*g*t^2, where g is the acceleration due to gravity.

Assuming the triangle to be a 3-4-5 triangle may not be accurate in this case. It is best to use the equations and given information to find the exact angle and height of the hill.