Question

A projectile is fired with a speel u at an angle with
the horizontal. Find ite speed when its direction of motion
makes an angle o, with the horizontal,​

Answer 1

Answer:

Let the speed be v when it makes an angle wih the horizontal.

as the horizontal component of velocity remains constant,

$v \cos( \alpha ) = u \cos( \alpha )$

OR

$v = u \cos( \alpha ) \sec( \alpha )$

Answer 2

$\Huge{\underline{\underline{\mathfrak{Correct \ Question \colon}}}}$

A projectile is fired with a speed u at an angle with respect to the horizontal. Find the speed of the projectile after time 't' with respect to the ground.

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

Let the initial speed of projection be u

Velocity of the object :

• With respect to vertical axis :

$\large{\boxed{\boxed{\sf{{u}_{y} = u \times sin \theta}}}}$

• With respect to ground :

$\large{\boxed{\boxed{\sf{{u}_{x} = u \times cos \theta}}}}$

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Let the speed of projectile be v after time t making an angle $\alpha$

Then,

• Vertical Component :

$\large{\boxed{\boxed{\sf{{v}_{y} = v \times sin \alpha}}}}$

• Horizontal Component :

$\large{\boxed{\boxed{\sf{{v}_{y} = v \times cos \alpha}}}}$

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Since,we require velocity with respect to the ground,the vertical components are not considered

Also,

Velocity of a projectile along x - axis remains uniform,which accounts to the fact that acceleration is zero.

Implies,

$\large{\sf{v \: cos \: \alpha = u \: cos} \theta} \\ \\ \large{\leadsto \: \sf{v = \frac{u \: cos \theta}{cos \alpha} }} \\ \\ \huge{ \leadsto \: \ \underline{\boxed{ \mathtt{v = u \: cos \theta sec \alpha}}}}$

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