An airplane is flying horizontally 100m above the ground at 50.0 m/s. Ignoring air resistance, how far before the target should an object be dropped?
h= gt²/2 =>
t=sqrt{2h/g},
s=vt
H=125m u=25m/s so H=u²sin²theta/2g then we will get value of sintheta and put it in formula R=u²sin2theta/g then we will get answer.
To calculate how far before the target an object should be dropped, we need to consider the horizontal distance covered by the object from the moment it is dropped until it reaches the target.
In this situation, the horizontal speed of the airplane (which we assume remains constant) would be the same as the horizontal speed of the dropped object. Therefore, the time it takes for the object to reach the target is the same as the time it takes for the airplane to cover the distance from the drop point to the target.
To determine the time it takes for the object to reach the target, we can use the equation:
time = distance / speed
Given that the airplane is flying at a horizontal speed of 50.0 m/s and that it needs to travel a horizontal distance equal to the drop point to the target, we can use these values to calculate the time.
Let's assume the distance from the drop point to the target is "x". Therefore, the time taken to cover this distance is:
time = x / 50.0
Since the object is in freefall, we can use the equation of motion under constant acceleration to calculate the vertical distance it would cover in this time.
Using the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
We can determine the time it takes for the object to reach the ground. In this case, the initial vertical velocity is 0 (since the object is dropped), and the acceleration due to gravity is approximately 9.8 m/s^2. So the equation becomes:
100 = (0 * t) + (0.5 * 9.8 * t^2)
Simplifying this equation gives us:
4.9t^2 = 100
Now we can solve for t, which will be the time it takes for the object to reach the ground. Once we have t, we can substitute it back into our original equation, time = x / 50.0, to solve for x, the horizontal distance between the drop point and the target.
By combining these calculations, we can determine how far before the target an object should be dropped.