Batman is standing on top of a 201 m tall building. He kicks off the building with a horizontal velocity of 10 m/s. Joker is driving a car towards the building at 40 m/s. What is batman's velocity at the point of impact (with respect to the ground)? How far away from the building does the impact occur? How long is Batman in the air?

i thought i could use delta x = Vx sqrt(2deltay/g) to find how far away the impact occured, but i'm not sure if that's what i was supposed to do. Please help asap! This homework is due tonight! Thanks!!!!!! :)

Justice.

To calculate Batman's velocity at the point of impact, we need to consider his initial horizontal velocity and the Joker's velocity. Let's break down the problem into a horizontal and vertical motion:

1. Batman's velocity at the point of impact:
Since Batman's initial horizontal velocity of 10 m/s does not change, his horizontal velocity at the point of impact remains the same. Therefore, Batman's horizontal velocity with respect to the ground is 10 m/s.

2. Distance from the building to the impact:
To determine how far away from the building Batman lands, we only need to consider his horizontal motion. Given that he has a horizontal velocity of 10 m/s and the Joker's car is approaching at 40 m/s, we know that the impact point will occur when the two velocities cancel each other out. Hence, the distance from the building to the impact is determined by the time it takes for the Joker's car to reach Batman's position.

To calculate the time it takes for the car to reach Batman's position, we need to divide the distance traveled by the car (201 m) by the relative velocity between Batman and the car (10 m/s + 40 m/s). Hence, the impact point is located 201 m / (10 m/s + 40 m/s) = 201 m / 50 m/s = 4.02 seconds away from the building.

3. Time of flight (how long Batman is in the air):
To find the time Batman spends in the air, we can use his vertical motion. We know the initial vertical velocity is 0 m/s (since Batman is only being launched horizontally off the building). We can use the formula: vertical displacement = (initial vertical velocity * time) + (0.5 * acceleration * time^2). Since Batman is subject to gravity, which causes an acceleration of -9.8 m/s^2 (negative because the acceleration is in the opposite direction of motion), and his vertical displacement is the height of the building (201 m), we can calculate the time of flight.

Using the equation: 201 m = (0 * t) + (0.5 * -9.8 m/s^2 * t^2), we can solve for t. Rearranging the equation, we have -4.9 t^2 = -201 m. Dividing both sides by -4.9 gives us t^2 = 41.02 seconds^2. Taking the square root of both sides, we find t = √(41.02 seconds^2) ≈ 6.4 seconds.

Therefore, Batman's velocity at the point of impact with respect to the ground is 10 m/s, the impact occurs 4.02 seconds away from the building, and Batman is in the air for approximately 6.4 seconds.