, you are on the right track with your approach to solving this problem. To find the final resting position of the ball, you will need to break the problem into smaller time intervals of 0.1 seconds. This will allow you to calculate the change in position and velocity for each interval and determine the final resting position.
Firstly, you will need to calculate the initial deceleration of the ball. This can be done using the formula a = F/m, where a is the acceleration, F is the force and m is the mass of the ball. In this case, the force is the rolling friction, which is given as 0.1. So, the initial deceleration can be calculated as 0.1/0.17 = 0.588 m/s^2.
Next, you will need to calculate the new speed and position for each time interval. This can be done using the equations v = u + at and s = ut + 1/2at^2, where v is the final velocity, u is the initial velocity, a is the acceleration, t is the time interval and s is the displacement. In this case, the initial velocity (u) in the x direction is 2.4 m/s and in the y direction is 0.7 m/s. So, for the first time interval of 0.1 seconds, the new speed in the x direction will be v = 2.4 + (-0.588)(0.1) = 2.34 m/s and the new position will be s = (2.4)(0.1) + 1/2(-0.588)(0.1^2) = 0.219 m. Similarly, for the y direction, the new speed will be v = 0.7 + (-0.588)(0.1) = 0.641 m/s and the new position will be s = (0.7)(0.1) + 1/2(-0.588)(0.1^2) = 0.063 m.
You will then repeat this process for each time interval, using the new speed and position as the initial values for the next interval. By the end, you will have a series of values for the final position of the ball at each time interval. The final resting position of the ball will be the last value in this series.
I hope this helps and good luck