00:01
Hi there, so for this problem we are told that a basket ball player is running with a speed that is 5 .05 meters per second toward the basket when he jumps into the earth to dunk the ball.
00:18
He maintains the same horizontal velocity while in the air at what horizontal distance for the basket in meters must he start his jump to reach his maximum height at the same time as he reaches the basket in meters.
00:35
Okay so first of all we're going to consider that that maximum height is equal to 0 .75 meters.
00:52
This should be given or else we cannot solve this problem.
00:57
Okay, now the speed for this and the well the initial x component of this speed is 5 .05 meters per second also that will be the final x component of the speed because we're told that it maintains this velocity horizontally.
01:25
Now we don't know what is the y component of the initial speed but we know that the final component of the y component of the final speed should be equal to zero because it is at the maximum height and at that moment, the y component of the speed is momentarily equals to zero.
01:54
Okay, so then with that said, what we need to do first is to obtain the initial speed in the y component.
02:03
For that, with the maximum height, and considering an acceleration due to gravity of 9 .8 meters per second squared, we can use the following equation from kinematics that the final y component of the speed is equal to the initial y component of the speed to the square plus 2 times the acceleration, in this case acceleration due to gravity, well, is minus this times the maximum height.
02:34
Okay now at the maximum height the final speed we know that is zero so we will have then that we can solve for the initial y component of the speed that will be the square root of two times acceleration due to gravity times that maximum height once we have this we can substitute the values two times nine point eight times the maximum height that is zero point seventy five we take square root of this.
03:03
So now let's use our calculator for this...