In a basketball game, a ball leaves a player's hand 6.1 m

downrange from the basket from a height of 1.2 m

below the level of the basket. if the initial velocity of

the ball is 7.8 m/s [55° above the horizontal] in line

with the basket, will the player score a basket? if not,

by how much will the ball miss the basket?

The player won't score and will miss the basket for 2.07m short.

Explanation:

We have a 2D proyectile problem, the basketball is moving at the same time in the X and Y axes, we can start by writing the information given:

The distance between the player and the basket is 6.1m that will be X.

The height where the basket was launched is 1.2m that will be the initial position or .

The initial velocity, is 7.8 m/s and its launched within 55° with the horizontal, that will be α.

We also need the equations of 2D movemnt

We can find the flying time t by using (1)

We can replace t in (2) and find what would be Y with that flying time, if it is equal to 3.05m the height of a basket the player would score, but if not he'll miss.

As the player won't score so we need to find how much will the ball miss the basket.

Using Y as 3.05m we can find the flying time necessary to score with equation 2.

we would obtain 2 answers for t, we have to chose the second one, remember that in a parabolic movement you pass 2 times through the same hight when you are going up and when you are going down so after finding the answers .

Finally replacing t found just before in (1) we can find the actual X, we will call it distance that the ball will travel.

and subtracting the two distances we will find by how much the ball will miss the basket.

So the player will miss the basket for 2.07 m.