a kid fires a slingshot pellet directly at a target that is far enough away to take one half second to reach. how far below the target does the pellet hit? how high above the target should she aim?
(1) However far an object would fall in 0.5 seconds. That is about 1.2 meters.
(2) Aim for a point above the target by an amount equal to the answer in (1)
To determine how far below the target the pellet hits, you need to understand the physics of projectile motion. The pellet is fired from a slingshot, which gives it an initial velocity. As it travels through the air, it follows a parabolic trajectory due to the force of gravity acting on it.
To calculate the vertical distance, we need to consider the time it takes to reach the target and the effect of gravity. In this case, the time of flight is one-half second. The equation for the vertical distance traveled by a projectile is given by:
d = v * t + (1/2) * g * t^2
Where:
- d is the vertical distance traveled by the pellet
- v is the initial vertical velocity (which is zero at the highest point of the trajectory)
- t is the time of flight
- g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
Since the initial vertical velocity is zero, the first term (v * t) becomes zero, simplifying the equation to:
d = (1/2) * g * t^2
Substituting the known values, we get:
d = (1/2) * 9.8 * (0.5)^2
d = (1/2) * 9.8 * 0.25
d ≈ 1.225 meters
Hence, the pellet will hit approximately 1.225 meters below the target.
To determine how high above the target she should aim, we need to analyze the symmetry of the projectile's trajectory. If the target is far enough away to take one-half second to reach, the total time of flight will be one second (as it takes the same time to ascend and descend). Therefore, she should aim the same distance above the target to compensate for the predicted vertical drop. In this case, she should aim approximately 1.225 meters above the target.