With what speed does the cart recoil if the projectile rises 2.1 m at its maximum height?

In this problem, we assume that the projectile was sent vertically upward. The maximum height reached is calculated through the equation,

H = (v²sin²θ) / 2g

where H is the maximum height, v is the velocity, θ is the angle (in this case, 90 degrees) and g is the gravitational constant.

Substituting the known values from the given,

2.1 = (v²) (1) / (2 x 9.8)

v = 6.415 m/s

Thus, the initial sped of the projectile is approximately equal to 6.42 m/s.