Question

A basketball shot is taken from a horizontal distance of 5m from the hoop. The height of the ball can be modelled by the relation h= -7.3t^2 + 8.25t +2.1, where h is the height in meters, and t is the time in seconds, since the ball was released

Answer 1

To determine the angle at which the ball must be thrown to hit the basket, we can use projectile motion equations. First, find the time it takes for the ball to reach the height of the basket. Next, calculate the horizontal distance traveled by the ball using the time found. Finally, use the horizontal distance and height difference to find the angle using trigonometric functions.

Step-by-step explanation:

To determine the angle at which the ball must be thrown to hit the basket, we can use projectile motion equations. First, we need to find the time it takes for the ball to reach the height of the basket. This can be done by setting the height equation equal to the height of the basket and solving for t.

Next, we can use the time we found to calculate the horizontal distance traveled by the ball. We know the initial speed of the ball and the time it takes to reach the basket's height.

Finally, we can use the horizontal distance and height difference between the ball and the basket to find the angle using trigonometric functions.

Answer 2

This is the concept of application of quadratic expressions. Given that the height of the ball is modeled by the equation;
h=-7.3t^2+8.25t+2.1+5
The time taken for the ball to hit the ground will be given as falls;
-7.3t^2+8.25t+7.1=0
to solve for t we use the quadratic formula;
t=[-b+/-sqrt(b^2-4ac)]/(2a)
a=-7.3, b=8.25, c=2.1
t=[-8.25+/-sqrt[8.25^2+4*7.3*7.1]/(-2*7.3)
t= -0.572
or
t=1.702
since there is not negative time we take the time taken for the ball to hit the ground will be: t=1.702 sec