A train moving with constant velocity 709ms−1 when a bullet strikes it in a direction making angle 37∘ with the train. The bullet enters one compartment at the corner farthest from the engine and passes out at the diagonally opposite corner. The compartment is 2.4 m long and 1.8 m wide. Choose the correct statement(s).

(1) Let ABCD is the top view of compartment.Here, AB = CD = 1.8 m and BC=AD=2.4m∴AC=(1.8)2+(2.4)2=3mand tan⁡α=2.41.8=43⇒ α=53∘Let vb is actual velocity of bullet.∴vbT=vb−vTor vb=vbT+vT⇒vbcos⁡37∘i^+vbsin⁡37∘j^=vbTcos⁡αj^+vbTsin⁡αj^+709i^⇒ 45vbi^+35vbj^=35vbTi^+45vbTj^+709i^∴45vb=35vbT+709and 35vb=45vbTor 34vb=vbT∴45vb=35×34vb+709⇒ 45vb−920vb=709or 16−920vb=709⇒ vb=709×207=2009ms−1=2009×185=80kmh−1(3) ∴vbT=34vb=34×80=60kmh−1∴t=ACVbT=3×10−560h360×60×60s=180s=3min