Chapter 15 - Kinetics of a Particle: Impulse and Momentum - Section 15.2 - Principle of Linear Impulse and Momentum for a System of Particles - Problems - Page 251: 23

$10.1ft/s$

The required speed can be determined as follows: $F=30+t^2=34$ $\implies t=2s$ Now we apply impulse momentum principle $mv_1+\Sigma \int ^{t_2}_{t_1} F_y dt=mv_2$ $\implies \frac{34}{32.2}(0)+\int ^{4}_{2} (30+t^2)dt-W\Delta t=(\frac{34}{32.2})v$ This simplifies to: $v=10.1ft/s$