On take off, the combined action of the engines and wings of an airplane exerts a(n) 7767 N force on the plane,directed upward at an angle of 59.1 degrees above the horizontal. The plane rises with constant velocity in the vertical direction while continuing to accelerate in the horizontal direction. The acceleration of gravity is 9.8 m/s^2. What is the weight of the plane? Answer in N.
What is the horizontal acceleration a? Answer in units of m/s^2.
constant velocity upward? No accelearation..
weight=mg=vertical force=7767*sin59.1
To find the weight of the plane, we need to first identify the force that opposes it. In this case, the force opposing the weight of the plane is the force exerted by gravity.
The weight of an object can be calculated using the formula:
Weight = mass × gravitational acceleration
Since the problem does not provide the mass of the plane, we need to use other information given to find it.
From the problem statement, we know that the combined action of the engines and wings of the airplane exerts a force of 7767 N directed upward at an angle of 59.1 degrees above the horizontal. This upward force is equal to the weight of the plane, which is opposed by the force of gravity.
Using trigonometry, we can resolve the upward force into horizontal and vertical components. The vertical component of the force will be equal to the weight of the plane:
Weight = upward force × cos(angle)
Weight = 7767 N × cos(59.1°)
Weight ≈ 7767 N × 0.5588
Weight ≈ 4341.9 N
Therefore, the weight of the plane is approximately 4341.9 N.
To find the horizontal acceleration, we can use the relationship between force, mass, and acceleration, which is described by Newton's second law of motion:
Force = mass × acceleration
In this case, the horizontal force is the force exerted by the engines and wings, which is 7767 N. We can rearrange the formula to solve for the horizontal acceleration:
acceleration = force / mass
Since the mass of the plane is not given, we cannot directly calculate the horizontal acceleration.