How Do You Solve Projectile Motion Problems?

The two main concepts to understand in order to solve projectile motion problems are that projectiles in flight constantly accelerate downward due to gravity and that projectiles fired at an angle have their velocities separated into horizontal and vertical components, which are used to derive different information. Using the numbers from the specific problem, one can use the formulas for these concepts to solve for the answer.

Many projectile motion problems in school give known quantities for the velocity and the angle of takeoff. For example, start off with an arrow that has been fired at an angle of 5 degrees at an initial velocity of 75 meters per second. Vertical/y-velocity is Vsin(theta), and horizontal/x-velocity is Vcos(theta), where V is the original velocity and theta is the angle. In this equation, the velocities of arrows x and y are 74.71 m/s and 6.53 m/s respectively. Then, calculate time of flight: 2vy/g, where vy is the y-velocity and g is the gravitational acceleration of 9.8 meters per second. The arrow stays in flight for 1.33 seconds. After one knows the time of flight, one can calculate the range by multiplying the x-velocity by the time of flight, which in this case is 99.36 meters. In most cases, one can round all quantities to two digits. Also, these equations assume no wind or air resistance.

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