Final answer:
The wheelbase of the truck can be calculated using the moments around the rear axle, leading to an approximate wheelbase of 1.90 meters.
Step-by-step explanation:
The student is asking about the wheelbase of a truck based on the weight distribution and the location of the center of gravity. To find the wheelbase of the truck, one can use the concept of moments or torques.
The wheelbase is the distance between the front and rear wheels, which is the point of support against the gravitational force that acts at the center of gravity.
Given that 57% of the weight is supported by the rear wheels and the center of gravity is 1.44m in front of the rear wheels, the moments around the rear wheels must equal the moments around the front wheels for the system to be in equilibrium. Using the formula:
Moment = Force × Distance
Let's denote the wheelbase as 'd' and let the total weight be 'W'. The moment about the rear axle due to the weight supported by the front wheels is 0.43 × W × d, and the moment about the rear axle due to the weight supported by the rear wheels is 0.57 × W × 0 (since it's at the pivot point). We have the distance from the front wheels to the center of gravity, 1.44m, and we need to find the total wheelbase 'd' where the front wheels are located. So:
0.43W × d = 0.57W × 1.44m
Dividing both sides by 0.43W, we find:
d = (0.57 × 1.44m) / 0.43
After calculating:
d ≈ 1.90m
Therefore, the wheelbase of the truck is approximately 1.90 meters.