A37.0-$kg$ body is moving in the direction of the positive x axis with a speed of 342 $m/s$ when, owing to an internal explosion, it breaks into three pieces. one part, whose mass is 5.0 $kg$, moves away from the point of explosion with a speed of 311 $m/s$ along the positive y axis. a second fragment, whose mass is 4.0 $kg$, moves away from the point of explosion with a speed of 402 $m/s$ along the negative x axis. what is the speed of the third fragment? ignore effects due to gravity.

Anew 2-lane road is needed in a part of town that is growing. at some point the road will need 4 lanes to handle the anticipated traffic. if the city's optimistic estimate of growth is used, the expansion will be needed in 4 years and has a probability of happening of 40%. for the most likely and pessimistic estimates, the expansion will be needed in 8 and 15 years respectively. the probability of the pessimistic estimate happening is 20%. the expansion will cost $ 4.2 million and the interest rate is 8%. what is the expected pw the expansion will cost?