spiderman is racing from the rooftop to catch the green goblin. he runs 125 m off a building 125 m tall to catch a robber coming out of the bank across thenstreet (30.0m away) if he is running at 10.0m/s will he hit the building, land the robber, or hit the ground before getting to the villain?
I got that his horizontal distance was 50.5m, but I don't understand if he will hit the building, land on him, or hit the ground before getting to him
To determine whether Spiderman will hit the building, land on the robber, or hit the ground before reaching the villain, we can analyze the horizontal and vertical components of Spiderman's motion separately.
First, let's calculate the time it takes for Spiderman to reach the horizontal distance of 30.0 m. We can use the equation: distance = speed × time.
Given that the horizontal distance (distance) is 30.0 m and the speed is 10.0 m/s, we can rearrange the equation to solve for time: time = distance / speed.
time = 30.0 m / 10.0 m/s = 3.0 s
So, it takes Spiderman 3.0 seconds to reach a horizontal distance of 30.0 m, which is where the robber is located.
Next, let's determine how far Spiderman falls vertically during this time. We can use the equation for vertical displacement: displacement = initial velocity × time + 0.5 × acceleration × time².
Given that the initial velocity (speed) in the vertical direction is 0 m/s (since Spiderman starts at the top of the building and falls freely), and the acceleration due to gravity is approximately 9.8 m/s², we can substitute these values into the equation:
displacement = 0 × 3.0 + 0.5 × 9.8 × (3.0)²
displacement = 0 + 0.5 × 9.8 × 9.0
displacement = 0 + 44.1
displacement = 44.1 m
Therefore, Spiderman would fall 44.1 meters vertically during the 3.0 seconds it takes to reach the robber.
Now, let's compare this vertical displacement to the height of the building, which is 125 m. Since Spiderman falls less than the height of the building, he will reach the ground before reaching the robber.
In conclusion, Spiderman will hit the ground before getting to the villain, indicating that he will not be able to catch the Green Goblin in this scenario.