One end of a light inextensible string is attached to a block. The string makes an angle of \(\theta°\) with the horizontal. The tension in the string is \(20\) N. The string pulls the block along a horizontal surface at a constant speed of \(1.5\) m s\(^{-1}\) for \(12\) s. The work done by the tension in the string is \(50\) J. Find \(\theta\). [3]

Question 1:
1 | EITHER:
WD = 20 cos θ × 1.5 × 12 (J) | (B1 | Using WD = Fd cos θ
[cos θ = 50/360] θ = .... | M1 | Use WD = 50 and solve for θ
θ=82(.0) | A1)
OR:
Power P = 50/12 = 4.1666… | (B1 | Using Power = WD/time
[50/12 = 20 cos θ × 1.5] θ = .... | M1 | Use P = Fv and solve for θ
θ=82 ( .0 ) | A1)
Total: | 3

One end of a light inextensible string is attached to a block. The string makes an angle of $\theta°$ with the horizontal. The tension in the string is $20$ N. The string pulls the block along a horizontal surface at a constant speed of $1.5$ m s$^{-1}$ for $12$ s. The work done by the tension in the string is $50$ J. Find $\theta$.
[3]

\hfill \mbox{\textit{CAIE M1 2017 Q1 [3]}}