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 7.8m [55 degrees 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 ball missed the basket by 1.6 meters

Explanation:

Projectile Motion

It's when an object is moving in a two-dimensional space, being thrown with an initial speed and angle respect to the horizontal direction. The horizontal distance traveled by the object is given by

And the vertical height above the level of the launch is

The basketball player throws the ball with initial speed at an angle of . The horizontal distance to the basket (as suggested by the 'downrange' word) is x=6.1 m. We need to find out if the ball reaches the basket at a height y=1.2 m above the launching point.

From the equation

We'll solve for t and find the flight time until the horizontal distance is reached by the ball

Now, we use this time to find y

The negative sign indicates the ball fell below the launching point, and missed the basket by

the average speed is 24.57 km/hr