Relative velocity Bumping into Crush You have finished

Relative velocity: Bumping into “Crush” You have finished your Physics homework in the resource room and are headed to the student center. You exit Allison Lab building and walk perpendicular to it. As you exit you see your Crush walking along the road adjacent to the building (shown, as I draw). For some reason, you know that your Crush walks at 2. 5 m/s. You also know that the two paths intersect at a 37 o angle. How fast should you walk (in the direction shown) so that you “casually” bump into your Crush at the point of intersection of the two paths? (Assume both of you walk at constant velocity. ) For some reason is the phrase you use to leave elements of the story to student imaginations!

Valentine Day Problem I am drawing as I narrate creating an atmosphere of drama and suspense. It seems long-winded and verbose in written form but didn’t while doing it in class. Due to poor drawing skills, the first time I drew Crush attached to the rope, it seemed like the rope was strangling him/her – huge laughter! You want your Crush to be your Valentine. But Crush has figured out that you have mastered relative velocity (students remember the previous problem) and are able to casually bump into him/her all the time. Now, as you approach Crush, s/he runs away from you, and goes up a hill. Crush does not know that the hill ends in a cliff and falls off the cliff. (Students “Aww…”. “Wait, there’s a happy ending!”) For some reason, there is a massless, frictionless pulley attached to the cliff and a rope hanging over it. (Huge laughter!) Crush gets hold of the massless, inextensible rope, hanging on for dear life. You are following Crush up the hill and as Crush holds on to the rope, you lunge forward and get hold of the other end of the rope. You are wearing a For some reason box jacket/sweater/shirt/dress of a certain coefficient of friction. (“You can buy these box sweaters/… online in various colors and friction coefficients”. ) Now, you know exactly how much Crush weighs, and you know – from past experience – the angle of the hill incline. As you hold the other end of the rope (while laying on the ground), you and your Crush are in equilibrium. (Assume stationary). What is the minimum coefficient of static friction you need your sweater/… to have to be able to save your Crush? Or, given a certain “mu”, find the range of masses your Crush can have. Many variations – let students get creative!

Given the masses for you, Crush and the rollerboard, what should v 1 be such that v 3 is 5 m/s? (Let the students assign the masses to themselves and their Crush – there will be two sets of answers for you to look at but in class this is very doable!) Variations include Crush jumping on in various different ways, velocities and angles. End the “rescue” with you and Crush jumping off in various scenarios e. g. you jump such that the rollerboard (with Crush on it) stops, or you and crush jump off in opposite directions, …