(a)Bolo, the human cannonball, is ejected from a 4.69-m long barrel. If Bolo (m
ID: 1962798 • Letter: #
Question
(a)Bolo, the human cannonball, is ejected from a 4.69-m long barrel. If Bolo (m = 79.1 kg) has a speed of 13.5 m/s at the top of his trajectory, 18.1 m above the ground, what was the average force exerted on him while in the barrel?(b) A snowboarder starts from rest and rides 36.17 m down a snow-covered slope that makes an angle of 32.05° with the horizontal and reaches the flat snow near the lift. How far will she travel along the flat snow if the coefficient of kinetic friction between her board and the snow is 0.03561?
Explanation / Answer
This problem has several steps:
i. First we need to find the speed Bolo left the barrel of the cannon. We know that at the top of his trajectory his y-velocity is zero, so the 13.5 m/s is his x-velocity. Since there is no acceleration in the x direction, we can assume the initial velocity in the x direction is 13.5 m/s.
To find his initial y velocity, we use one of the equations of motion:
(v1)2 = (v0)2 + 2a (y1 - y0)
Where a = g, y0 = 0, y1 = 18.1m, v1 = 0. We want to find v0. We make the assumption that the 18.1m in the problem is above the top of the cannon, not above the ground (but this is a common mistake made by problem writers).
0 = (v0)2 + 2 (9.8 m/s2) (-18.1 m)
v0 = sqrt(2 (9.8 m/s2) (18.1 m)) = 18.83 m/s
Now we have the x component (13.5 m/s) and the y component (18.83 m/s) of his initial velocity. We can now find his initial velocity.
v = sqrt(vx2 + vy2) = sqrt((13.5 m/s)2 + (18.83 m/s)2) = 23.17 m/s
ii. We now need to find the acceleration in the cannon. We no longer need to consider x and y components. Using the equation of motion used above, we can calculate the acceleration he felt in the cannon:
(v1)2 = (v0)2 + 2a (x1 - x0)
Where v1 = 23.17 m/s, v0 = 0 m/s, x1 = 4.69 m, x0 = 0 m. a is what we are solving for.
(23.17 m/s)2 = 2a (4.69 m)
a = (22.56 m/s)2 / (2 * 4.69 m)
= 57.25 m/s2
We now use the definition of force to calculate the force exerted on him in the cannon:
F = ma
= 79.1 kg * 57.25 m/s2
= 4528.51 N
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