The world record for the discus throw is 74.08m , set by Jürgen Schult in 1986.If he had been competing, not on earth, but on Mars, where the acceleration due to gravity is 0.379 what it is on earth, and if he had thrown the discus in exactly the same way as on earth, what would be his Martian record for this throw? Assume that the discus is released essentially at ground level
Ignoring aerodynamic effects, the maximum distance a thrown object can travel over level ground is V^2/g, where V is the launch velocity and g is the acceleration of gravity.
This happens when the object is thrown at a 45 degree angle from the horizontal. The same equation applies on Mars, where g is 0.379 times as large as on Earth. That makes the distance 1/.379 = 2.64 times farther than it is on earth.
To find out the Martian record for the discus throw, we need to consider the difference in gravity between Earth and Mars. The acceleration due to gravity on Mars is given as 0.379 times that of Earth.
Here's how we can calculate Jürgen Schult's Martian record for the throw:
1. First, we need to determine the equivalent Martian distance that would have been covered if he had thrown the discus with the same technique and initial conditions as on Earth.
2. The formula to calculate the distance covered by a projectile thrown horizontally is given by:
distance = ((velocity)^2 / (2 * g))
where velocity is the initial velocity and g is the acceleration due to gravity.
3. On Earth, the distance of the discus throw was 74.08m.
So, on Mars, we can set up the equation:
74.08m = ((velocity)^2 / (2 * (0.379 * g)))
4. Rearrange the equation to isolate the initial velocity:
velocity^2 = 74.08m * 2 * (0.379 * g)
velocity^2 = 0.5676144 * g
velocity = sqrt(0.5676144 * g)
5. Now, substitute the acceleration due to gravity on Mars (0.379 * g) into the equation:
velocity = sqrt(0.5676144 * (0.379 * g))
6. Calculate the square root of this value to find the velocity:
velocity = sqrt(0.214866976 * g)
7. Once we have the velocity, we can calculate the Martian distance traveled:
distance = ((velocity)^2 / (2 * (0.379 * g)))
distance = ((sqrt(0.214866976 * g))^2 / (2 * (0.379 * g)))
Here, g refers to the acceleration due to gravity on Mars.
By plugging the appropriate value for g on Mars into the equation, we can find out Jürgen Schult's Martian record for the discus throw.