Momentum, Collisions and Explosions Legacy Problem #23 Guided Solution
Problem*
Hayden (m=24.3-kg) is gliding along the sidewalk on his skateboard at 8.6 ft/s. As he travels under a low-hanging branch of the tree where Matthew is sitting, he grabs the 4.5-kg bag of soccer balls from Matthew's hands. Determine the speed of Hayden immediately after grabbing the bag of soccer balls.
Audio Guided Solution
A good problem solver reads a problem carefully and develops a mental picture of what's going on and then identifies the known and the unknown quantities and uses conceptual reasoning skills and physics principles to plot out a strategy from the known information to the unknown information. Here we have a picture of two boys, one in a tree and one on a skateboard. The boy on the skateboard is moving along with a known mass and a known speed when he collects a bag from the boy in the tree. Afterwards, having more mass now, the boy on the skateboard is moving slower than he was before. And what we wish to do is determine the post-collision, if we call it that, speed of the boy on the skateboard. So we're going to use the principle that the pre-collision momentum of the boy and the bag is equal to the post-collision momentum of the boy and the bag. Before the collision, it's only the boy on the skateboard that has momentum. And that momentum can be found if you multiply the mass of the boy times the speed at which the boy is moving, 24.3 kilograms times the 8.6 feet per second. When you do that multiplication, you get the momentum of the boy, which comes out to be 208.98 kilograms times a foot per second. This is the momentum before the collision and it is also the momentum of both objects after the collision. So for the after-collision momentum, we would say that it is the mass of the boy times the velocity plus the mass of the bag plus its velocity. Since the boy is holding the bag, those two objects move together with the same velocity and we'll call that velocity v. So we would say that after the collision, the total momentum is 24.3 times v for the boy plus 4.5 times v for the bag. That sums to 28.8 v. And 28.8 v, the momentum after the collision, should equal the momentum before the collision, which was calculated as 208.98 kilograms foot per second. If you divide through by 28.8, you would get the velocity of the boy and the bag after the collision. It comes out to be 7.256 feet per second and that can be rounded to two significant digits.
Solution
7.3 ft/s
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(m = 1.50 \unit{kg}\), \(v_i = 2.68 \unit{\meter\per\second}\), \(F = 4.98 \unit{\newton}\), \(t = 0.133 \unit{\second}\), \(v_f = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Momentum, Collisions and Explosions at The Physics Classroom Tutorial.