how does the launch angle affect the range of the marble?

Answer 1

The vertical component of the launch angle determines how long the marble stays airborne.

The horizontal component determines the horizontal distance it travels per unit of time.

If you are airborne very long, but with no lateral movement, range is zero. If you have a huge lateral speed but no airborne time, range is zero.

The best ratio turns out to be approximately 45 degrees, equal amounts of horizontal and vertical speed.

Answer 2

enable's say the projectile is shot at a speed of v at an attitude of ?. Then the horizontal area of the initial speed is v cos?, and the vertical element is v sin?. The horizontal element not in any respect adjustments considering that no horizontal forces act on the projectile in the time of flight. The vertical element will substitute because the gravitational stress performing on the projectile is vertical. assume the projectile is fired from the inspiration. The horizontal position x(t) more beneficial linearly with time (because no forces act on it). x(t) = v cos? * t in spite of the undeniable fact that, the vertical position quickens downward: y(t) = v sin? * t - a million/2 * g * t^2 those equations merely come from kinematics. The flight is over at the same time as the projectile hits the floor (y = 0): 0 = v sin? * t - a million/2 * g * t^2 a million/2*g*t = v sin? t = (2v sin?)/g this promises the time at the same time as the projectile hits the floor. The horizontal distance travelled in this time is: X = v cos? * (2v sin?)/g X = v^2/g * 2cos?sin? yet 2cos?sin? = sin (2?) from a trig identity so X = (v^2 * sin(2?))/g the position X = the gap travelled by technique of the projectile. the biggest that sin (2?) will be is a million. this occurs at the same time as ? = 40 5 ranges because sin (2*40 5) = sin (ninety) = a million. So 40 5 ranges will maximize X, the gap travelled by technique of the projectile. do not hear to the first guy i am going to tell he of direction has little or no information of physics. What he stated is garbage.

Answer 3

just imagine you launch a marble straigh up. How far is the range? not much.

Now, imagine you lauch the marble with an angle, it will go further.

Answer 4

Assuming no air resistance, maximum range achieved when launched at 45deg to the horizontal.

Answer 5

Yes, it does