Finding height and time from angle and velocity

[wunderbred5]

A toy rocket is launched with a velocity of 30 at an angle of 50 deg. How would I find the height, distance, and time from that? Please help...

 

[Shooting Star]

Seeing that your question has not been shifted to the homework section, I’ll give you some idea. But the whole thing can be found in any high school mechanics book.

I assume that the toy rocket doesn’t have a propulsion system and is simply given an initial velo.
You have not given the unit of velo, so put the proper units for all the quantities.

If the angle with the horizontal is ‘x’ radians, then after time t,

horizontal dist traveled = 30*(cos x)*t, and

height of the rocket = 30*(sin x)*t –(g/2)*t^2.

Convert 50 degrees to radians.

 

[ogb p]

To find the height, distance, and time from the given information, you can use the equations of projectile motion. First, you can find the initial vertical velocity (Vy) using the given velocity and angle. This can be done by using the trigonometric function sine (sin), where Vy = 30*sin(50) = 23.09 m/s.

Next, you can use the equation for height (h) at a given time (t), which is h = Vy*t - 0.5*g*t^2, where g is the acceleration due to gravity (9.8 m/s^2). Since the rocket is launched at ground level, the initial height (h0) is 0. Therefore, the equation becomes h = 23.09*t - 4.9*t^2.

To find the time (t) it takes for the rocket to reach its maximum height, you can use the fact that at the highest point, the vertical velocity becomes 0. So, you can set Vy = 0 and solve for t, giving you t = 23.09/9.8 = 2.36 seconds.

To find the maximum height (hmax), you can substitute the found time (t) into the equation for height, giving you hmax = 23.09*2.36 - 4.9*2.36^2 = 27.2 meters.

Finally, to find the horizontal distance (d) traveled by the rocket, you can use the equation d = Vx*t, where Vx is the initial horizontal velocity (30*cos(50) = 19.3 m/s). Therefore, d = 19.3*2.36 = 45.6 meters.

In summary, the height of the rocket at any given time can be found using the equation h = Vy*t - 0.5*g*t^2, the maximum height can be found by setting Vy = 0 and solving for t, the horizontal distance can be found using the equation d = Vx*t, and the time can be found using the equation t = Vy/g. I hope this helps!