Question

Ethan throws a ball into the air from a cliff that is 152.4 m high with an initial velocity of 4 m/s. How long does it take for the ball to hit the ground?

Answer 1

Based on the fact that matter will accelerate 9.8 m/s when going down due to gravity, we first subtract 4 m/s, this gives 148.4 meters left. Now, for each second, we add 9.8 m/s to the velocity. First, the speed will increase to 13.8 m/s, so at 2 seconds, the ball will have traveled 17.8 meters down, with 134.6 meters to go. At 3 seconds, the ball will be traveling at 23.6 m/s, so at 3 seconds it's traveled 41.4 meters and has 111 meters to go. At 4 seconds, it's traveling at 33.4 m/s, so 74.8 total meters now, and has 77.6 meters to go. At 5 seconds, it travels at 43.2 m/s, so now its 118 total meters. Now at 6 seconds, it would travel 53 m/s but there isn't that amount of meters left. So we can make a proportion of x/10=34.4/53 (10 for the number of deciseconds in a second and 34.4 for the number of meters left). This means that 53x=344, or x=6.49. Now we can convert this amount of time from a decisecond to a decimal of a second, meaning that the amount of time it takes for the ball to hit the ground is 5 seconds plus 0.649 seconds, or 5.649 seconds

The answer is 5.649 seconds, respectively.

Hope this helps.