A 1.5 kg ball moving at 5.0 m/s makes an elastic, off-centre collision with an identical ball at…

Step 1. Second ball's direction. $90^\circ - 35^\circ = 55^\circ$ on the other side of the first line.

Step 2. Speeds. The velocity triangle is right-angled: $v_1 = 5.0\ \text{m/s}\cos 35^\circ = 4.10\ \text{m/s}$ and $v_2 = 5.0\ \text{m/s}\sin 35^\circ = 2.87\ \text{m/s}$.