A parachutist, after bailing out, falls $50 \mathrm{m}$ without friction. When the parachute opens, it decelerates at $2 \mathrm{m} {\mathrm{s}}^{-2}$. He reaches the ground with a speed of $3 \mathrm{m} {\mathrm{s}}^{-1}$. At what height did he bailout? 

You are on the roof of the physics building, $46.0 \mathrm{m}$ above the ground. Your physics professor, who is $1.80 \mathrm{m}$ tall, is walking alongside the building at a constant speed of $1.20 \mathrm{m} {\mathrm{s}}^{-1}$. If you wish to drop a flower on your professor's head, where should the professor be when you release the flower? Assume that the flower is in free fall. (Take g = $9.8 \mathrm{m} {\mathrm{s}}^{-2}$)
 

Two particles are simultaneously released from points $A$ and $D$ as shown in figure. How should the value of $H$ be adjusted in order that the two particles collide? Neglect dissipative forces.

At time $t=0$, a student throws a set of keys vertically upward to her sorority sister, who is in a window at distance $h$ above. The second student catches the keys at time $t$.

(a) With what initial velocity was the keys thrown?

(b) What was the velocity of the keys just before they were caught?

A railroad flatcar is travelling to the right at a speed of $15 \mathrm{m} {\mathrm{s}}^{-1}$ relative to an observer sitting on the ground. Someone is riding a scooter on the flatcar (as shown in the figure). The velocity of a scooter with respect to a car is $10 \mathrm{m} {\mathrm{s}}^{-1}$. What is the velocity of the scooter relative to the observer on the ground in case $\left(\mathrm{a}\right)$ and case $\left(\mathrm{b}\right)$ as shown in the figure?

Two parallel rail tracks run north to south. The train $A$ moves north with a speed of $54 \mathrm{km} {\mathrm{h}}^{-1}$ and the train $B$ moves south with a speed of $90 \mathrm{km} {\mathrm{h}}^{-1}$. A monkey running on the roof of the train $A$ against its motion (with its velocity of $18 \mathrm{km} {\mathrm{h}}^{-1}$ with respect to the train $A$). What is the velocity of the monkey, $\left(\mathrm{a}\right)$ as observed by an observer on the ground? $\left(\mathrm{b}\right)$ as observed by an observer moving in train $B$?