Question

two projectiles are fired from same point on the ground with the same speed at angle of projection 53 and 37 with the horizontal respectively. which one of the following is true?​

Answer 1

Given:

2 projectiles are fired from the same spot on the ground with the same speed at angles of projection 53° and 37° with horizontal.

To find:

True statement among:

• They will have same range
• They will have same max height
• Their time of journey will be same.

Calculation:

Let range be denoted by R.

For the 1st Projectile:

$R1 = \dfrac{ {u}^{2} \sin(2 \times {53}^{ \circ} ) }{g}$

$= > R1 = \dfrac{ {u}^{2} \sin( {106}^{ \circ} ) }{g}$

For the 2nd Projectile:

$R2= \dfrac{ {u}^{2} \sin(2 \times {37}^{ \circ} ) }{g}$

$= > R2 = \dfrac{ {u}^{2} \sin( {74}^{ \circ} ) }{g}$

$= > R2 = \dfrac{ {u}^{2} \sin( {180}^{ \circ} - {106}^{ \circ} ) }{g}$

$= > R2 = \dfrac{ {u}^{2} \sin( {106}^{ \circ} ) }{g}$

$= > R2 = R1$

Hence range will be same.

• As a general rule , two projectiles thrown with same velocity and with complementary angle of projections will have the same range.

• But the time period and max Height for the projectiles will be different.