An archer puts a 0.34 kg arrow to the bowstring. An average force of 220 N is exerted to draw the string back 1.3 m. Assume that air resistance is negligible. If the arrow is shot straight up, how high does it rise?
I am confused at how to find the distance that it will rise.
The work done drawing the bow is
W = (average force)*(distance pulled)
= 286 Joules
Set that equal to the potential energy gained at highest altitude, H
M g H = 286 J
H = 286/(0.34*9.8) = ____?
Note that kinetic energy does not enter into the equation at highest altitude because the arrow is temporarily motionless there.
Two girls with masses of 50.0 kg and 70.0 kg are at rest on frictionless in-line skates. the larger girl pushes the smaller girl so that the latter rolls away at a speed of 10.0 m/s. What is the effect of the action on the larger girl? What is the impulse that each girl exerts on the other?
dunno
To find the height the arrow rises when shot straight up, we can use the principle of conservation of energy.
First, let's calculate the potential energy stored in the bowstring when it is fully drawn back. The potential energy (U) is given by the formula:
U = mgh
Where:
m is the mass of the arrow (0.34 kg in this case)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height the arrow will reach (what we are trying to find)
Now, the potential energy stored in the bowstring can be calculated as:
U = (0.34 kg) * (9.8 m/s^2) * h
Next, let's consider the work done by the archer to draw the string back. The work (W) is given by the formula:
W = F * d * cos(theta)
Where:
F is the average force exerted (220 N in this case)
d is the distance the string is drawn back (1.3 m in this case)
theta is the angle between the force and the displacement (in this case, since the arrow is shot straight up, theta = 0)
Now, the work done by the archer can be calculated as:
W = (220 N) * (1.3 m) * cos(0)
W = 220 N * 1.3 m * 1
Since the work done by the archer is equal to the potential energy stored in the bowstring, we can equate the two equations:
W = U
220 N * 1.3 m = (0.34 kg) * (9.8 m/s^2) * h
Simplifying the equation:
286 N*m = 3.332 kg*m/s^2 * h
Simplifying further:
286 N*m = 3.332 N * h
Now we can solve for h by dividing both sides of the equation by 3.332 N:
h = 286 N*m / 3.332 N
h ≈ 85.8 m
Therefore, the arrow will rise to a height of approximately 85.8 meters when shot straight up.