How much time does the toy rocket spend the air, and how far from its launch point does it land in the field?Īnswer: The first thing that must be found to solve this problem is the initial velocity in the x and y directions. Its initial velocity has a magnitude of 20.0 m/s. Therefore, the velocity (magnitude and direction) of the ball after 5.00 s was 51.24 m/s, -72.98° down from the horizontal.Ģ) A toy rocket is launched in a flat field, aimed at an angle 60.0° up from the horizontal (x) axis. If the horizontal direction is 0.0 radians, the angle can be found with the equation: Though it was not asked for in the question, it is also possible to find the direction of the velocity as an angle. The magnitude of the velocity is 51.24 m/s. To find the magnitude of the velocity, the x and y components must be added with vector addition: In projectile motion problems, up is defined as the positive direction, so the y component has a magnitude of 49.0 m/s, in the down direction. The x component of the velocity after 5.00 s is: The ball was kicked horizontally, so v xo = 15.0 m/s, and v yo = 0.0 m/s. Once these two components are found, they must be combined using vector addition to find the final velocity. After 5.00 s, what is the magnitude of the velocity of the ball?Īnswer: The velocity of the ball after 5.00 s has two components. The initial velocity of the ball is 15.0 m/s horizontally. G = acceleration due to gravity (9.80 m/s 2)ġ) A child kicks a soccer ball off of the top of a hill. Vertical velocity = initial vertical velocity - (acceleration due to gravity)(time) Horizontal velocity = initial horizontal velocity Horizontal distance = (initial horizontal velocity)(time) The horizontal and vertical velocities are expressed in meters per second (m/s). The units to express the horizontal and vertical distances are meters (m). Velocity is a vector (it has magnitude and direction), so the overall velocity of an object can be found with vector addition of the x and y components: v 2 = v x 2 + v y 2.
The trajectory has horizontal (x) and vertical (y) components. The path the object follows is determined by these effects (ignoring air resistance). A projectile is an object that is given an initial velocity, and is acted on by gravity.
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