To find the angle to the horizontal that the man must pull, we can use the formula for the force of tension, which is T = mg sinθ, where T is the tension force, m is the mass of the box, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle between the rope and the horizontal.
First, we need to find the magnitude of the force of tension, which is equal to the force required to accelerate the box at 1.27 m/s^2, in the direction of the pull. This can be calculated using Newton's second law of motion, F = ma, where F is the force, m is the mass, and a is the acceleration.
In this case, the force required to accelerate the box at 1.27 m/s^2 is 15 kg x 1.27 m/s^2 = 19.05 N.
Now, we can plug this value into the formula for the force of tension: 19.05 N = 65N sinθ.
Solving for sinθ, we get sinθ = 19.05N / 65N = 0.293.
To find the angle, we can use the inverse sine function, sin^-1, on both sides: θ = sin^-1(0.293) = 17.1 degrees.
Therefore, the man must pull the rope at an angle of 17.1 degrees to the horizontal in order to accelerate the box at 1.27 m/s^2, assuming that the force of friction can be ignored.
