A person can jump a maximum horizontal
distance (by using a 45 projectile angle) of 5 m on Earth.
What would be the maximum range on Mars,
where the acceleration due to gravity is 0.38 g?
6.05
To find the maximum range on Mars, we first need to understand the factors that influence the range of a projectile.
The range of a projectile depends on its initial velocity, launch angle, and the acceleration due to gravity. In this case, the launch angle is given as 45 degrees, and the acceleration due to gravity on Mars is specified as 0.38 g.
To determine the maximum range on Mars, we can use the following formula:
Range = (Initial velocity^2 * sin(2θ)) / g
In this formula:
- Initial velocity is the speed at which the projectile is launched.
- θ (theta) is the launch angle.
- g is the acceleration due to gravity on Mars.
We are given the maximum horizontal distance on Earth, which is 5 meters. With this information, we can find the initial velocity.
To calculate the initial velocity, we rearrange the formula:
Initial velocity = Square root((Range * g) / sin(2θ))
Now we can substitute the given values into the equation:
θ = 45 degrees
g = 0.38 g = 0.38 * 9.8 m/s^2 = 3.724 m/s^2 (acceleration due to gravity on Mars)
Range = 5 meters
Plugging in these values, we get:
Initial velocity = Square root((5 * 3.724) / sin(2 * 45))
Now calculate the numerator:
Numerator = (5 * 3.724) = 18.62
Now calculate the denominator:
denominator = sin(2 * 45) = sin(90) = 1
Now substitute these values to find the initial velocity:
Initial velocity = Square root(18.62 / 1)
Initial velocity = Square root(18.62) ≈ 4.313 m/s
Now we have the initial velocity, we can use it to find the maximum range on Mars:
Range = (Initial velocity^2 * sin(2θ)) / g
Range = (4.313^2 * sin(2 * 45)) / 3.724
Range = (18.62 * 1) / 3.724 ≈ 4.995 m
Therefore, the maximum range on Mars, where the acceleration due to gravity is 0.38 g, is approximately 4.995 meters.