Question

You are part of a search and rescue mission that has been called out to look for a lost explorer. You've found the missing explorer, but you're separated by a 153 m high cliff and a 35 m wide raging river. To save his life, you need to get a 4 kg package of emergency supplies across the river. Unfortunately, you can't throw the package hard enough to make it across. Fortunately, you happen to have a 0.6 kg rocket intended for launching flares. Improvising quickly, you attach a sharpened stick to the front of the rocket, so that it will impale itself into the package of supplies. What minimum speed must the rocket have just before impact in order to save the explorer's life?

We'll break this into pieces. This is a combination collision + projectile motion question.
How long is the package in the air? (Hint the y info will tell you how much time passes before it loses all its height.)
s
What must be the x velocity of the package + rocket so that they make it across the river?
m/s
What must be the initial velocity of the rocket, before the collision with the package?
m/s

Answer 1

time to fall from cliff h Į gf? 9 t = 0.152 = 5.587 sec 9.8 5.587 Horizontal distance = 3510m horizontal speed = 35.0 ms U= 6.963 mst according to law of conservation of linear me 0.6 V + uxo = (4+0.6) x 6.263 V= Ub x 6.263 0.6 V= 38.812 = 48.02 met sockel must have speed 48.02 mst

Thanks for asking.

I hope it helps you.