Question

A body projected vertically upwards with a velocity U returns to the starting pointd in second calculate the value of u if g=10m/s​

Answer 1

Correct Question:

• A body is projected vertically upwards with velocity u returns to starting point in 4 sec. If g=10m/s², the value of u is.

Answer:

• The value of u is 20 m/s.

Explanation:

Given that,

• Acceleration due to gravity (g) = 10 m/s²
• Time (t) = 4 sec

Now, use formula of time of flight,

$\red \bigstar \boxed{\sf \red \: t = \frac{2u}{g} }$

[ Putting values ]

$\longrightarrow \sf \: 4 = \frac{2u}{10} \\ \\ \longrightarrow \sf 2u = 4 \times 10 \\ \\ \longrightarrow \sf 2u = 40 \\ \\ \longrightarrow \sf u = \frac{40}{2} \\ \\ \: \: \longrightarrow \: \sf \underbrace{u = 20 \: ms {}^{ - 1} } \: \: \green \bigstar$

Answer 2

Correct question :

A body projected vertically upwards with a velocity U returns to the starting point in 4 seconds. calculate the value of u if g=10m/s​

Given :

• g = 10 m/s²
• Body returns to the starting point in 4 seconds (t)

To find :

• Initial velocity of body

Concept :

As the body returns to it's initial position so we will use time of flight formula . Time of flight of projectile motion is given as the time from when the object is projected to the time it reaches the surface.

Solution :

Time of flight is given by,

$\longmapsto\boxed{\boxed{\sf{Time \ (t) = \dfrac{2u}{g} }}}$

Substituting values,

$\longmapsto\sf 4 = \dfrac{2u}{10} \\\\ \\ \longmapsto\sf 4 * 10 = 2u \\\\ \\ \longmapsto\sf 2u = 40 \\\\ \\ \longmapsto\sf u = \dfrac{40}{2} \\\\ \\ \longmapsto\boxed{\underline{\overline{\bf{\mid{Initial \ velocity \ (u) = 20 \ ms^{-1} }}}}}$

$\therefore\underline{\textsf{Initial velocity of body i.e. u = {\textbf{20 m/s}}}}$