A

Step 1: Convert energy from calories to Joules. The energy content of the bananas is 1000 cal. Using the mechanical equivalent of heat:
\( 1000 \text{ cal} \times 4.2 \text{ J/cal} = 4200 \text{ J}

Step 2: Use the potential energy formula. The potential energy (PE) when the boy jumps is given by:
\( PE = mgh \)
where \( m = 50 \text{ kg} \), \( g = 10 \text{ m/s}^2 \), and \( h \) is the height.
Setting the energy used to the potential energy:
\( 4200 = 50 \times 10 \times h
\( 4200 = 500h
\( h = \frac{4200}{500} = 8.4 ext{ m}

Step 3: Conclude. Therefore, the height he can jump is 8.4 m.