Answer the following problem solving. Use GUFSA to get the answers. 1. An airplane fly horizontally 2500 m above the ground at 300 km/h drops a cargo at a target on the ground. Determine where the cargo will strike the ground.
Given :
Unknown:
Formula:
Solution:
Final Answer:
Calculate the centripetal force and acceleration of a 3.0 Kg mass tied in a rope and swung in a circle of radius 0.75 m, which is moving at a velocity of 4.0 m/s?
Given:
- An airplane is flying horizontally at a height of 2500 m above the ground.
- The speed of the airplane is 300 km/h.
- The cargo is dropped from the airplane.
Unknown:
- The location where the cargo will strike the ground.
Formula:
- We can use the formula of distance, speed, and time: distance = speed × time.
Solution:
Step 1: Convert the speed from km/h to m/s.
- 1 km/h = 1000/3600 m/s = 5/18 m/s.
- Speed = 300 km/h × (5/18 m/s) = 83.33 m/s.
Step 2: Determine the time it takes for the cargo to hit the ground.
- Since the cargo is dropped vertically, its horizontal speed is not relevant.
- The time it takes for the cargo to hit the ground can be determined by finding the time it takes for an object to free fall from a height of 2500 m.
- We can use the formula: distance = (1/2) × acceleration × time^2, where acceleration = 9.8 m/s^2 (acceleration due to gravity).
- 2500 m = (1/2) × 9.8 m/s^2 × time^2.
- Solving for time, we get: time = sqrt((2 × distance) / acceleration)
- time = sqrt((2 × 2500) / 9.8) = 6.37 seconds.
Step 3: Calculate the horizontal distance covered by the cargo.
- Distance = Speed × Time = 83.33 m/s × 6.37 s = 531.67 meters.
Final Answer:
The cargo will strike the ground at a horizontal distance of 531.67 meters from the point directly beneath the airplane.
To solve this problem using GUFSA (Given, Unknown, Formula, Solution, Final Answer) method, let's break it down step by step:
Given:
- The airplane is flying horizontally 2500 m above the ground.
- The speed of the airplane is 300 km/h.
Unknown:
- The location where the cargo will strike the ground.
Formula:
To determine where the cargo will strike the ground, we need to calculate the time it takes for the cargo to fall and the horizontal distance it travels during that time.
The time it takes for the cargo to fall can be determined using the formula:
time = sqrt((2 * distance) / g)
Where:
- distance is the vertical distance the cargo falls (2500 m)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
The horizontal distance the cargo travels can be calculated using the formula:
horizontal distance = (speed of the airplane) * time
Solution:
1. Calculate the time it takes for the cargo to fall:
- distance = 2500 m
- g = 9.8 m/s^2
time = sqrt((2 * 2500) / 9.8)
2. Calculate the horizontal distance the cargo travels:
- speed of the airplane = 300 km/h (convert to m/s by dividing by 3.6)
- time (from step 1)
horizontal distance = (300 / 3.6) * time
Final Answer:
The location where the cargo will strike the ground will be the horizontal distance calculated in step 2.