The range is given by x = V 0 2 sin(2θ) / g Problem 3 A projectile is to be launched at an angle of 30° so that it falls beyond the pond of length 20 meters as shown in the figure.Ī) What is the range of values of the initial velocity so that the projectile falls between points M and N? Substitute x and y by their expressions above to obtain The relationship between the coordinate x and y on the incline is given by The x and y components of the displacement are given by The projectile hits the incline plane at point M.Ī) Find the time it takes for the projectile to hit the incline plane. Problem 2 A projectile is launched from point O at an angle of 22° with an initial velocity of 15 m/s up an incline plane that makes an angle of 10° with the horizontal. The magnitude V of the velocity is given by The components of the velocity at t = 2 V0 sin(θ) / g are given by The components of the velocity at t are given by The horizontal range is the horizontal distance given by x at t = t2. Time of flight = t2 - t1 = 2 (20) sin(θ) / g = 1.72 seconds.Ĭ) In part c) above we found the time of flight t2 = 2 V 0 sin(θ) / g. Maximum height y (0.86) = 20 sin(25°)(0.86) - (1/2) (9.8) (0.86) 2 = 3.64 metersī) The time of flight is the interval of time between when projectile is launched: t1 and when the projectile touches the ground: t2. T = V 0 sin(θ) / g = 20 sin(25°) / 9.8 = 0.86 secondsįind the maximum height by substituting t by 0.86 seconds in the formula for y That is when the projectile changes from moving upward to moving downward.(see figure above) and also the animation of the projectile. The height of the projectile is given by the component y, and it reaches its maximum value when the component V y is equal to zero.

Problem 1 An object is launched at a velocity of 20 m/s in a direction making an angle of 25° upward with the horizontal.Ī) What is the maximum height reached by the object?ī) What is the total flight time (between launch and touching the ground) of the object?Ĭ) What is the horizontal range (maximum x above ground) of the object?ĭ) What is the magnitude of the velocity of the object just before it hits the ground?Ī) The formulas for the components V x and V y of the velocity and components x and y of the displacement are given by These solutions may be better understood when Solutions and detailed explanations to projectile problems are presented.

Projectile motion problems