Final answer:
The speed and direction of the object after the impulse occurs are 2.11 m/s to the left.
Step-by-step explanation:
To find the object's speed and direction after the impulse occurs, we can use the principle of conservation of momentum. Since there is no external force acting on the system, the total momentum before the impulse is equal to the total momentum after the impulse.
The initial momentum is given by: p = mass × velocity = (4.50 kg) × (-3.60 m/s) = -16.2 kg⋅m/s
The impulse is given by the change in momentum: Impulse = final momentum - initial momentum. Therefore, final momentum = initial momentum + Impulse = -16.2 kg⋅m/s + 6.70 Ns = -9.50 kg⋅m/s
Finally, the final velocity can be calculated by dividing the final momentum by the mass of the cart: velocity = -9.50 kg⋅m/s / 4.50 kg = -2.11 m/s
Therefore, the object's speed after the impulse occurs is 2.11 m/s to the left.