#Advanced projectile motion equations simulator

You can then solve for minimum v o and maximum v o.Īnswer: Minimum v o = 15.824 m/s, maximum v o = 17.041 m/s To determine the total time t set Δd y = 0, and solve for t. When the ball begins to enter the trunk, the horizontal distance Δd x traveled by the ball is given by Δd x = ( v ocos θ) t, which is also equal to the distance d o+ Vt for minimum v o and d o+ L+ Vt for maximum v o, where t is the total time.

#Advanced projectile motion equations simulator

I created a projectile motion simulator to solve problems like this. You need to solve this with numerical methods which accounts for the effects of air resistance. This projectile motion problem involves initially horizontal projectile motion, which means there is no initial vertical velocity component to consider. This projectile motion problem involves strictly vertical projectile motion, which means there is no horizontal velocity component to consider. Given known Δd x = ( v ocos θ) t, with v o and θ known, find t and then use this t to find Δd y using the equation for vertical displacement ( Δd y) on the projectile motion page. You must choose the largest time t corresponding to the stage of the flight where the projectile is moving downward.Īnswer: h = 1.276 m, Δd x = 6.472 m, t = 0.747 s Note that there are two solutions for time t which correspond to Δd y = 1 m. This problem is similar to problem 2 so the hint for it applies here as well. To find the range you first need to find the total time t the projectile is airborne, and then you can use this time to find the range Δd x = v x t where v x = v ocos θ.Īnswer: h = 1.276 m, Δd x = 17.556 m, t = 2.027 s There is a specific equation on the projectile motion page which you can use to solve for the maximum height when v 2y = 0. We know that at maximum height there is zero vertical velocity ( v 2y = 0). To find maximum height set v 1y = v osin θ. Obtain an explicit expression for time t based on the quantities v 1y and Δd y, and find θ so that Δd x is maximum. Referring to the projectile motion page, set v x = v ocos θ and v 1y = v osin θ.

Hints And Numerical Answers For Projectile Motion Problems Hint and answer for Problem # 1 The hints and answers for these projectile motion problems will be given next. Assume that the initial height of the ball is equal to the height of the ball at the instant it begins to enter the trunk. If the initial horizontal distance from the back of the truck to the ball, at the instant of the kick, is d o = 5 m, and the truck moves directly away from the ball at velocity V = 9 m/s (as shown), what is the maximum and minimum velocity v o so that the ball lands in the trunk. It is intended that the ball lands in the back of a moving truck which has a trunk of length L = 2.5 m. Compare this to the answer in problem 2.Ī ball is kicked at an angle θ = 45°. Account for air resistance, with drag coefficient equal to 0.47, projected frontal area equal to 0.01 m 2, density of air equal to 1.2 kg/m 3, and mass of projectile equal to 0.1 kg. What is the flight time?įind the maximum height and range for v o = 10 m/s, and θ = 90°.įind the maximum height and range for v o = 10 m/s, θ = 0, and Δd y = -5 m.įind the maximum height and range for v o = 10 m/s, θ = 30°, and Δd y = -10 m. What is the flight time?įind Δd y for v o = 10 m/s, θ = 30°, and Δd x = 15 m. The displacement Δd y corresponds to the stage of the projectile flight where it is moving downward. What is the flight time?įind the maximum height and range for v o = 10 m/s, θ = 30°, and Δd y = 1 m. Use g = 9.8 m/s 2.įor problems 1-6 and 8, ignore air resistance in your calculations.įor Δd y = 0 and for any given v o find θ so that the range ( Δd x) is maximum.įind the maximum height ( h) and range for v o = 10 m/s, θ = 30°, and Δd y = -10 m. Refer to the figure below (along with sign convention shown), for problems 1-7.

I also provide hints and numerical answers for these problems. The required equations and background reading to solve these problems is given on the projectile motion page.

On this page I put together a collection of projectile motion problems to help you understand projectile motion better.