# Range Equation: Launching a 78g Basketball at 8.4 m/s

• delfam
In summary, to find the speed at which the player must give the ball, the range equation is used by solving for the general form, which involves the initial velocity, angle, and acceleration due to gravity. However, the given equation is missing a term and needs to be adjusted to accurately solve for the velocity.
delfam

## Homework Statement

a 78g basketball is launched at 40.4 degrees at at 14.2m, ball is released at same height as basket. what speed must the player give the ball.

## Homework Equations

deltax = 2(Vo^2)sin(2theta)

## The Attempt at a Solution

14.2 = 2Vo^2 * (.9871360) / 9.8
69.58 = Vo^2(.9871360)
Vo^2 = 70.48
Vo = 8.4

Hi delfam,

delfam said:

## Homework Statement

a 78g basketball is launched at 40.4 degrees at at 14.2m, ball is released at same height as basket. what speed must the player give the ball.

## Homework Equations

deltax = 2(Vo^2)sin(2theta)

I don't believe this equation is quite right. What should it be?

## The Attempt at a Solution

14.2 = 2Vo^2 * (.9871360) / 9.8
69.58 = Vo^2(.9871360)
Vo^2 = 70.48
Vo = 8.4

is it just (Vo^2) and not 2(Vo)^2

Try solving for the general form of the range equation by taking
$$x(t)=v_0\cos(\theta)t \,\,\,\,(1)$$ and
$$y(t)=y_0+v_0\sin(\theta)t-\frac{gt^2}{2} \,\,\,\,(2)$$
solving (2) for the final time ($$t_f$$), and then substituting $$t_f$$ into (1) and simplifying.

Hint: your expression is missing a term from one of these equations.

Last edited:
m/s

The range equation is a useful tool for calculating the distance an object will travel when launched at a certain velocity and angle. In this case, the 78g basketball is launched at 8.4 m/s and at an angle of 40.4 degrees. Using the range equation, we can calculate the distance the ball will travel, which is 14.2m in this scenario. However, the question asks for the speed the player must give the ball in order for it to reach this distance. Using the same equation, we can rearrange it to solve for the initial velocity (Vo) of the ball. Plugging in the given values, we get Vo = 8.4 m/s. Therefore, the player must give the ball an initial speed of 8.4 m/s in order for it to reach a distance of 14.2m at an angle of 40.4 degrees.

## What is the range equation for launching a 78g basketball at 8.4 m/s?

The range equation for launching a 78g basketball at 8.4 m/s is R = (v2sin2θ)/g, where R is the range, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

## How do you calculate the range of a basketball launched at 8.4 m/s?

To calculate the range of a basketball launched at 8.4 m/s, plug in the values of v = 8.4 m/s and θ into the range equation R = (8.42sin2θ)/9.8 m/s2. The launch angle can be measured in degrees or radians, as long as it is consistent with the units of v.

## What is the maximum range of a basketball launched at 8.4 m/s?

The maximum range of a basketball launched at 8.4 m/s can be found by setting the launch angle θ to 45 degrees. This results in a maximum range of R = (8.42sin90)/9.8 m/s2 = 3.41 meters.

## How does the range of a basketball launched at 8.4 m/s change with different launch angles?

The range of a basketball launched at 8.4 m/s will vary with different launch angles. As the launch angle increases, the range will also increase until it reaches a maximum at 45 degrees. Any angles greater than 45 degrees will result in a shorter range, and any angles less than 45 degrees will also result in a shorter range.

## What other factors can affect the range of a basketball launched at 8.4 m/s?

Aside from the initial velocity and launch angle, other factors that can affect the range of a basketball launched at 8.4 m/s include air resistance, wind speed and direction, and the surface on which the basketball is launched. These factors can alter the trajectory of the basketball and ultimately affect its range.

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