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.
In the .190 sec, the pellet falls
4.9(.19)^2 = .177m
What about the second part of the answer? And where did you get the 4.9 from?
y=gt²/2 =9.8•0.19²/2 =4.9•0.19² = …
For finding the distance you need v(x)
s=v(x)• t
To find how far below the target the pellet hits, we need to first determine the vertical displacement of the pellet during its flight. We can use the equation for vertical displacement (d) without considering air resistance:
d = (1/2) * g * t^2
Where:
d = vertical displacement
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time of flight (0.190 s)
Plugging in the values:
d = (1/2) * 9.8 m/s^2 * (0.190 s)^2
d ≈ 0.1691 m
Therefore, the pellet hits approximately 0.1691 meters below the target.
Now, to determine how high above the target Brittany should aim, we need to consider that the pellet will follow a parabolic trajectory. We need to find the maximum height of the trajectory to ensure the pellet reaches the target.
The maximum height of a projectile launched at an angle can be determined using the following equation:
h = (v^2 * sin^2(θ)) / (2 * g)
Where:
h = maximum height
v = initial velocity
θ = launch angle
g = acceleration due to gravity (approximately 9.8 m/s^2)
Since the problem states that the pellet was thrown "directly" at the target, we can assume that it was launched horizontally, meaning the launch angle (θ) is 0 degrees.
Furthermore, since we are given the time of flight (0.190 s) and the target distance, we can use the equation for horizontal displacement:
d = v * t
Where:
d = horizontal displacement (target distance)
v = initial velocity
t = time of flight
Rearranging this equation for v:
v = d / t
Plugging in the values:
v = (target distance) / (time of flight)
Now we can use the maximum height equation:
h = [(d / t)^2 * sin^2(0)] / (2 * g)
Since sin(0) = 0, the equation simplifies to:
h = 0 / (2 * g)
h = 0
Therefore, Brittany should not aim above the target since the pellet will hit exactly at the same height as the target.