Which one among the following diagrams may correctly represent the motion of a skydiver during a jump ?
- (a)Speed curves up to about 50 m/s, holds steady, then drops abruptly and settles at a low steady value until landing
- (b)Speed rises in a straight line to about 50 m/s, then falls in a straight line to near zero
- (c)Speed rises in a straight line to about 50 m/s and falls in a straight line back to zero
- (d)Speed curves smoothly up to about 50 m/s and then curves smoothly back down to zero
Answer
Why
Correct — A. Follow what actually happens in a jump and check it against the printed graphs.
Free fall. The skydiver accelerates under gravity, but air resistance grows with speed, so the acceleration falls away. The speed therefore rises along a curve that flattens, not a straight line.
Terminal velocity. When drag has grown to equal the weight, the net force is zero and the speed stops changing — a plateau, at roughly 50 m/s.
The parachute opens. Drag jumps enormously, far exceeding the weight, and the skydiver decelerates hard. On the graph this is an abrupt drop.
Descent and landing. A new, much lower terminal velocity is reached and held — a low but non-zero steady speed, since the skydiver is still coming down.
Graph (a) is the only one with all four: curved rise, plateau, sharp drop, low steady finish.
Why the others are wrong
- (b)Speed rises in a straight line to about 50 m/s, then falls in a straight line to near zero — A straight rise means constant acceleration, which would require no air resistance — and without air resistance there would be no terminal velocity and no parachute effect at all. It also lacks any plateau.
- (c)Speed rises in a straight line to about 50 m/s and falls in a straight line back to zero — The same straight-line error, and worse at the end: it brings the speed to zero while the skydiver is still in the air. A parachute slows the fall, it does not stop it.
- (d)Speed curves smoothly up to about 50 m/s and then curves smoothly back down to zero — The curved rise is right, but there is no plateau at terminal velocity and no abrupt change when the parachute opens — and again the speed returns to zero in mid-air rather than settling at the slower descent rate.
Concept
A falling body is acted on by its constant weight and by air resistance, which grows with speed. While drag is less than weight the body accelerates, but by less and less; when drag equals weight the net force is zero and the body falls at a constant terminal velocity. Opening a parachute multiplies the drag, producing a sharp deceleration to a new, much lower terminal velocity.
Every option reaches about the same peak speed, so the peak is not the discriminator — the SHAPE is. Two checks settle it. First, is the rise curved? Air resistance guarantees it, so any straight-line rise is out. Second, where does the graph end? A parachutist lands at a few metres per second, not at rest in mid-air, so a graph returning to zero before landing is out. Only one option survives both.
Key facts
- Air resistance increases with speed, so acceleration decreases during free fall.
- Terminal velocity is reached when drag equals weight; the speed then stays constant.
- A free-fall terminal velocity for a skydiver is roughly 50 m/s.
- Opening the parachute sharply increases drag and lowers the terminal velocity.
- The skydiver lands at a small non-zero speed, not at rest in the air.
Curved rise, plateau, sharp drop, low steady finish — only graph (a) has all four.
Study next
Common traps
- Choosing a straight-line rise, which ignores air resistance.
- Letting the speed fall to zero while the skydiver is still airborne.
- Missing the plateau at terminal velocity before the parachute opens.
NDA prints several speed-time graphs for a physical situation — walk through the stages of the real motion and strike out every graph that gets one of them wrong.
Related PYQs
The figure given below shows the direction of the two forces P and Q acting on a skydiver: Which one among the following statements is correct about the two forces?
- (a) Force P is caused by the gravity and force Q is caused by the friction
- (b) When the force P is bigger than the force Q, the speed of the skydiver remains the same
- (c) After the parachute opens, force P remains the same while force Q increases
- (d) After the parachute opens, force P decreases while force Q increases
Answer(c) After the parachute opens, force P remains the same while force Q increases
The same jump analysed through forces rather than a graph — the downward weight P and the upward drag Q, and what happens to each when the parachute opens.
Practice
- practice — not a real PYQ
A body falling through air reaches terminal velocity when
- (a)its weight becomes zero
- (b)air resistance equals its weight
- (c)air resistance becomes zero
- (d)its acceleration equals g
Answer(b) air resistance equals its weight — the net force is then zero and the speed stops changing. - practice — not a real PYQ
When a parachute opens, the terminal velocity of the falling person
- (a)increases
- (b)decreases
- (c)becomes zero
- (d)is unchanged
Answer(b) decreases — the much larger area greatly increases drag, so balance with weight occurs at a lower speed.