A small plane takes off with a constant speed of 130 km/h at an angle of 37 degrees. In 3.00 s, how high is the plane and what horizontal distance has it traveled from the lift-off point.
I know I should convert 130km/h into meters per second, but after that I am stuck.
Can you please help me? Thank you.
Sorry I wasted your time! I understand it now!
Of course! Let's break down the problem step by step.
First, we need to convert the speed of the plane from kilometers per hour to meters per second. To do this, we can use the following conversion factor:
1 kilometer = 1000 meters
1 hour = 3600 seconds
So, to convert 130 km/h to meters per second:
130 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 36.11 m/s
Now that we have the speed of the plane in meters per second, we can move on to calculating the horizontal distance and height.
Let's consider the horizontal motion first. The plane is traveling at a constant speed, so we can use the equation:
Distance = Speed * Time
The time given is 3.00 seconds, and the speed is 36.11 m/s.
Distance = 36.11 m/s * 3.00 s = 108.33 meters
Therefore, the horizontal distance the plane has traveled from the lift-off point is 108.33 meters.
Now let's move on to calculating the height of the plane. We can use trigonometry to find the height.
Given that the plane takes off at an angle of 37 degrees, the height of the plane can be found using the equation:
Height = Distance * tan(angle)
The distance traveled is the same as the horizontal distance we calculated earlier, which is 108.33 meters. The angle is 37 degrees, but remember to convert it to radians before using the tangent function.
Angle in radians = angle in degrees * (π / 180)
37 degrees * (π / 180) = 0.6458 radians
Height = 108.33 m * tan(0.6458) ≈ 89.74 meters
Therefore, the height of the plane is approximately 89.74 meters.
To summarize:
- The horizontal distance the plane has traveled from the lift-off point is approximately 108.33 meters.
- The height of the plane is approximately 89.74 meters.
I hope this helps! Let me know if you have any further questions.