Well, five answers for only five points is pretty slim. But I've already got a lot of points, and your plea for help sounds so desperate, that I think I ought to jump in here and relieve some of your pain.
These aren't difficult problems. The bummer is that whoever wrote them got so interested in his dinosaur stories that he kind of hid the actual Math and Physics under all kinds of stuff that doesn't matter.
1). Speed = (distance covered) / (time to cover the distance)
= (56.9 miles) / (68.2 minutes)
= (56.9 / 68.2) miles/minute
= 0.834 mile per minute.
BUT ... the question wants to know the speed in 'mph' ... miles per hour.
Well ... there are 60 minutes in an hour. If 0.834 mile in covered in 1 minute, then 60 times as much would be covered in 1 hour.
(0.834 mile/minute) x (60 minute/hour) = 50.06 mile/hour<span>
</span> Rounded to no decimal places = 50 mph
2). Use the same formula:
Speed = (distance covered) / (time to cover the distance)
= (189 meters) / (211 seconds)
= (189 / 211) meters/seconds
= 0.8957 meters/second
Round to 3 decimal places: 0.896 m/s
3). The attacker jumped from 24.8 meters away. He already covered half of the distance. How far away is he now ? 1/2 of 24.8 m = 12.4 m . He still has 12.4 meters left to go.
He's moving at 82.3 meters per second. When will he arrive here ?
Time = (distance) / (speed)
= (12.4 meters) / (82.3 m/s)
= (12.4 / 82.3) seconds
= 0.1506 second
Two decimal places: 0.15 second
4). Distance = (speed) x (time)
= ( 237 km/hr) x (16.8 seconds) .
Do you see the problem here ? We have the distance covered in an hour, but we need to know how much distance is covered in only 16.8 seconds. We really need to work out the speed in (meters per second).
OK. 237 km = 237,000 meters, so the speed is 237,000 meters/hour.
1 hour is 3,600 seconds. So the speed is only one 3600th of 237,000 meters in 1 second.
(237,000 meters/hour) x (1 hour / 3600 seconds) = 65.8333 m/s
Distance = (speed) x (time)
= (65.8333 meter/second) x (16.8 seconds)
= (65.8333 x 16.8) meters
= 1106 meters.
5). This is a nasty trick question. The whole story is irrelevant, and we don't even care how far Vinny dropped.
Anything that drops on Earth falls with the acceleration of gravity. It doesn't matter how big or heavy or small or light it is. Everything falls with the acceleration of gravity on Earth ... about 9.8 m/s² .
