A girl throws a slingshot pellet directly at a target that is far enough away to take 0.9 s to reach. How far below the target does the pellet hit?
m
How high above the target should she aim?
m
How far does anything fall in 0.9 s ??
-(1/2)(9.8) t^2 = - 4.9(.81) = - 3.97 m
Of course, if she's throwing it upwards, it's going to rise for .45 sec and then fall for .45 sec.
How far above the target she will aim depends on how far away the target is. It will also affect how hard she has to throw it.
To find the distance below the target where the pellet hits, we can use the formula for the vertical motion of an object under constant acceleration:
d = V₀t + 1/2at²
Where:
d is the distance traveled
V₀ is the initial velocity (in this case, 0 m/s as the pellet is thrown vertically)
t is the time taken (0.9 s)
a is the acceleration due to gravity (-9.8 m/s²)
Let's calculate the distance below the target where the pellet hits:
d = (0)(0.9) + 1/2(-9.8)(0.9)²
= -4.41 m
Therefore, the pellet hits approximately 4.41 meters below the target.
To find the height above the target where she should aim, we need to calculate the maximum height reached by the pellet. The time taken to reach the maximum height is half the total time taken to reach the target:
t_max = 0.9 / 2
= 0.45 s
Using the same formula as before, we can calculate the height above the target:
d_max = (0)(0.45) + 1/2(-9.8)(0.45)²
= -0.99 m
Therefore, she should aim approximately 0.99 meters above the target.
To determine how far below the target the pellet hits, we need to consider the vertical motion of the pellet. The pellet is subject to the force of gravity, which will cause it to accelerate downward.
We can use the equation for vertical motion: d = v*t + (1/2)*a*t^2, where:
- d is the vertical displacement of the pellet
- v is the initial vertical velocity of the pellet (which is 0 since it was thrown horizontally)
- t is the time taken for the pellet to reach the target (0.9 s)
- a is the acceleration due to gravity (-9.8 m/s^2, assuming a standard value on Earth)
Plugging in the given values, we have:
d = (0 * 0.9) + (1/2) * (-9.8) * (0.9^2)
Simplifying the equation:
d = 0 + (-4.41)
We find that the pellet hits approximately 4.41 meters below the target.
To determine how high above the target the girl should aim, we need to find the vertical displacement of the pellet from the target. Since the pellet hits below the target, the girl should aim higher to compensate for its downward motion.
One way to determine the required height is to consider the time it takes for the pellet to reach its maximum height. At the maximum height, the vertical velocity becomes 0 before it starts falling back down.
Using the equation for vertical motion: v = u + at, where:
- v is the final vertical velocity (0 m/s at the maximum height)
- u is the initial vertical velocity when the pellet is thrown (0 m/s)
- a is the acceleration due to gravity (-9.8 m/s^2, assuming a standard value on Earth)
- t is the time taken for the pellet to reach its maximum height
Rearranging the equation to solve for t:
t = (v - u) / a
Plugging in the given values:
t = (0 - 0) / -9.8
Since the initial and final velocities are both 0, the time taken to reach the maximum height is 0 seconds.
Therefore, the girl should aim her slingshot pellet at the same height as the target.