A projectile of mass 1.000 kg is shot straight up with an initial speed of 23.0 m/s.
(a) How high would it go if there were no air resistance?
i got 26.99, which is correct
(b) If the projectile rises to a maximum height of only 17.8 m, determine the magnitude of the average force due to air resistance.
i got 4.32.......and it's not right.. help please
for part b
kinetic energy at ground - F * h = potential energy at top
(1/2) (1) (23)^2 - F (17.8)= 1*9.81*17.8
264.58 - 17.8 F = 174.6
F = 5.05 Newtons I get
To determine the height a projectile would reach without air resistance, we can use the kinematic equation for vertical motion. Since the projectile is shot straight up, we can use the equation:
vf^2 = vi^2 + 2ad
Where:
vf = final velocity (which is zero at the maximum height)
vi = initial velocity (given as 23.0 m/s)
a = acceleration due to gravity (approximated as -9.8 m/s^2, taking negative as it acts against the motion)
d = displacement (which is the height we want to find)
Rearranging the equation to solve for displacement:
d = (vf^2 - vi^2) / (2a)
Substituting the given values:
d = (0^2 - 23.0^2) / (2 * -9.8)
d = -529 / -19.6
d ≈ 27 meters (rounded to two decimal places)
So, the maximum height the projectile would reach without air resistance is approximately 27 meters.
Now let's move on to part (b).
To determine the magnitude of the average force due to air resistance, we need to consider the work-energy principle. When the projectile rises to a maximum height of 17.8 meters, some of its initial kinetic energy is converted into work against air resistance.
The work done by air resistance can be calculated using the formula:
Work = force * distance
In this case, the distance is the displacement (∆d) between the starting point and the maximum height (17.8 m). We can use the equation:
Force * ∆d = ∆KE
Since force is constant with respect to distance, we can rearrange the equation to solve for force:
Force = ∆KE / ∆d
The change in kinetic energy (∆KE) is equal to the initial kinetic energy (KEi) since the final kinetic energy (KEf) is zero at maximum height. The initial kinetic energy can be calculated using the formula:
KE = 1/2 * mass * velocity^2
Substituting the given values:
KE = 1/2 * 1.000 kg * (23.0 m/s)^2
KE ≈ 270 J (rounded to three significant figures)
Now we can calculate the magnitude of the average force due to air resistance:
Force = KEi / ∆d
Force = 270 J / 17.8 m
Force ≈ 15.17 N (rounded to two significant figures)
Therefore, the magnitude of the average force due to air resistance is approximately 15.17 N.