# Solving Maximum Range Throw for Astronaut on Earth and Planet with g1

• Naeem
In summary, the conversation discusses the maximum distance a ball can be thrown by an astronaut in a space suit, and how to achieve the greatest range by determining the angle and speed at which the ball is thrown. It also explores how far the ball can be thrown on a planet with a different gravitational acceleration, and the height the ball will reach on a "maximum range" trajectory. To calculate the height, the formula X = V sqrt (2H/g) can be used, where the initial velocity component that points upward is v1 and the acceleration is a. Using the formula v_{2}^2 = v_{1}^2 + 2ad, the velocity at maximum height can be calculated and plugged into the equation to
Naeem
Q. An astronaut in his space suit can throw a ball a maximum distance dmax = 8 m on the surface of the earth.

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a) For a given speed of the ball, what angle to the horizontal q (in degrees) will yield the greatest range?
q = ° 45 *

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b) If the ball is thrown at this same angle q, what speed will produce this greatest range (8 m) ?
v = m/s *
sqrt (78.48) OK

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c) How far can he throw the ball on a planet where g1 = 19 m/s2?
xp = m *
9.81*8/19 OK

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d) What height will the ball reach on this "maximum range" trajectory? (on the planet where g1 = 19 m/s2)
hmax = m
3.91 NO

Need help with part d,

I think we need to use the formula , X = V sqrt (2H/g), if yes, what to plug in,

Pl. Help

for d
Vertical ONLY
what is your initial velocity COMPONENT that points upward? that's v1. What is the velocity of the ball at it's maximum height? what is the acceleration?
use this formula
$$v_{2}^2 = v_{1}^2 + 2ad$$
and don't forget about a sign convention, take one direction (up or down) to be positive and the other to be negative. You cannot take the square root of a negative number - you have toi get a REAL number

At the maximum height, v2 = 0

d = -v1^2/2(-9.81)

v1= v1sin(45)

I get 1.027m

## What is the maximum range throw for an astronaut on Earth and a planet with g1?

The maximum range throw for an astronaut on Earth and a planet with g1 can be calculated using the formula: R = (v^2*sin(2α))/g, where R is the range, v is the initial velocity, α is the launch angle, and g is the acceleration due to gravity. This formula applies to both Earth and planets with a surface gravity of g1.

## How does the launch angle affect the maximum range throw on Earth and a planet with g1?

The launch angle plays a crucial role in determining the maximum range throw on both Earth and a planet with g1. The optimal launch angle for maximum range is 45 degrees on Earth and varies for different planets with g1, depending on their surface gravity.

## What is the relationship between initial velocity and maximum range throw on Earth and a planet with g1?

There is a direct relationship between the initial velocity and the maximum range throw on both Earth and a planet with g1. As the initial velocity increases, the maximum range also increases. This is because a higher initial velocity allows the object to travel further before gravity pulls it back down.

## How does the surface gravity of a planet affect the maximum range throw for an astronaut?

The surface gravity of a planet has a significant impact on the maximum range throw for an astronaut. The higher the surface gravity, the shorter the maximum range will be. This is because a higher surface gravity means that the object will experience stronger gravitational pull, causing it to fall back to the ground sooner.

## What are some factors that can affect the accuracy of calculating the maximum range throw on Earth and a planet with g1?

Some factors that can affect the accuracy of calculating the maximum range throw include air resistance, wind speed, and the shape and weight of the object being thrown. These factors can alter the trajectory and velocity of the object, resulting in a different maximum range throw than predicted by the formula.

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