If a body is thrown upwards tends to go it to a height of 10mtrs.if initial velocity is doubled what will be the height reached
initial energy will be 4x as much, so it will go 4x as hight
To find the new height reached when the initial velocity is doubled, we need to understand the relationship between the initial velocity, height reached, and other relevant variables.
When a body is thrown upwards, the height it reaches is determined by the initial velocity and the acceleration due to gravity. The key variables involved are:
1. Initial velocity (u): The velocity at which the body is thrown upwards.
2. Final velocity (v): The velocity of the body when it reaches its maximum height.
3. Acceleration due to gravity (g): The acceleration acting on the body, which is approximately 9.8 m/s² on Earth.
4. Height reached (h): The maximum height attained by the body.
We can use the equations of motion to derive the relationship between these variables. One of the relevant equations is:
v² = u² + 2gh
Here, v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and h is the height reached.
Since the body is thrown upwards and eventually comes to rest at its maximum height, the final velocity (v) will be zero. This allows us to simplify the equation:
0 = u² + 2gh
Now, if we double the initial velocity (u), we can substitute the new value into the equation:
0 = (2u)² + 2gh'
Here, h' represents the new height reached.
Simplifying further:
0 = 4u² + 2gh'
We know that the original height reached was 10 meters (h = 10). Plugging in the values:
0 = 4u² + 2(9.8)h'
Now, we can solve for h' by rearranging the equation:
h' = -2(9.8)h / (4u²)
Substituting the known values:
h' = -2(9.8)(10) / (4u²)
Using this formula, you can calculate the new height reached when the initial velocity is doubled by plugging in the appropriate values for u.