NEET Physics — Laws of Motion

A $0.4 \, \text{kg}$ ball at $40 \, \text{m/s}$ hits a wall at $45^\circ$ and rebounds at $30^\circ$ with speed $35 \, \text{m/s}$. What is the impulse along the wall? (Take $\sin 45^\circ = \cos 45^\circ = 0.707$, $\sin 30^\circ = 0.5$, $\cos 30^\circ = 0.866$)

A $1000 \, \text{kg}$ car on a $30^\circ$ banked road ($\mu_s = 0.35$) turns at radius $50 \, \text{m}$ while decelerating at $2 \, \text{m/s}^2$ tangentially. What is the maximum speed? (Take $g = 10 \, \text{m/s}^2$, $\tan 30^\circ = 0.577$)

A $3.5 \, \text{kg}$ block on a horizontal surface ($\mu_k = 0.25$) is connected to a $5.5 \, \text{kg}$ mass over a pulley. A $8 \, \text{N}$ force aids the $3.5 \, \text{kg}$ block. What is the acceleration? (Take $g = 10 \, \text{m/s}^2$)

A $8 \, \text{kg}$ block on a $60^\circ$ incline ($\mu_k = 0.25$) is connected to a $5 \, \text{kg}$ mass over a pulley. A $20 \, \text{N}$ force at $30^\circ$ to the incline opposes the $8 \, \text{kg}$ block. What is the acceleration? (Take $g = 10 \, \text{m/s}^2$, $\sin 60^\circ = 0.866$, $\cos 60^\circ = 0.5$, $\sin 30^\circ = 0.5$, $\cos 30^\circ = 0.866$)

A $7.6 \, \text{kg}$ block on a $60^\circ$ incline ($\mu_k = 0.15$) is pulled upward by a $9.6 \, \text{kg}$ mass over a pulley. What is the acceleration? (Take $g = 10 \, \text{m/s}^2$, $\sin 60^\circ = 0.866$, $\cos 60^\circ = 0.5$)