Question

As you are headed to class, your friend leans out the window of your apartment 10 m above you andshouts that you took her car keys rather than your own. Since you are in a hurry, you decide to tossyour friend’s keys up to her while she drops your keys down to you. You throw the keys just hardenough to reach her outstretched hand. At what height above you will the two sets of keys passeach other?

Known:

Unknown:

Strategy:

Solution:

Answer 1

the velocity with which i have thrown the keys from the ground can be found using newton 3rd equation

since final velocity is zero

therefore u2 = 2*g*s = 2*10*10 we get u = 10*sqrt[2] m/s

distance travelled by keys thrown by friend is given by

s1 = [1/2]*g*t²

distance travelled by keys thrown by me is given by

s2 = u*t - [1/2]*g*t²

also s1 + s2 = 10 m

adding oth the equations we get u*t = 10

we get t = 1 / sqrt[2] sec put value of t in first equation

s1 = [1/2] * g*t²

we get s1 = [1/2] * 10 * 0.5 = 2.5 m from the window or 7.5 m from the ground