Brittany throws a slingshot pellet directly at a target that is far enough away to take 0.190 s to reach. How far below the target does the pellet hit? Enter m as unit.
How high above the target should she aim? Enter m as unit.
To find the distance below the target where the pellet hits, we can use the equation of motion for vertical motion:
d = vit + (1/2)at^2
Where:
d = distance traveled
vi = initial vertical velocity
t = time taken
a = acceleration (in this case, due to gravity)
Since the pellet is thrown directly at the target, the initial vertical velocity is 0 m/s. The acceleration due to gravity is approximately -9.8 m/s^2 (negative because it acts in the opposite direction to the motion).
Using the values given, we have:
vi = 0 m/s
t = 0.190 s
a = -9.8 m/s^2
Substituting the values into the equation:
d = 0(0.190) + (1/2)(-9.8)(0.190)^2
Simplifying:
d = (1/2)(-9.8)(0.0361)
d = -0.176 m
Therefore, the pellet hits the target 0.176 m below.
To find how high above the target Brittany should aim, we can consider the symmetry of projectile motion. Since the pellet reaches the same height on the way up as it does on the way down, we can simply double the calculated distance below the target.
So, the height above the target she should aim is:
Height = 2 * 0.176
Height = 0.352 m
Therefore, Brittany should aim approximately 0.352 m above the target.