Question

A projectile is fired from a gun near the surface of Earth. The initial velocity of the projectile has a vertical component of 90 meters per second and a horizontal component of 49 m/s. How long will it take the projectile to reach the highest point in its path?
A100.s B20.s C10.s
D5.s

Answer 1

For this we only need to observe vertical component. Vertical component is 90 meters/s
The gravity is decresing vertical component at rate of 9.80 m/s because gravity acceleration is 9,80 m/s^2

Simply by deviding starting vertical speed and gravitational acceleration we get time required for  projectile to stop gaining altitude.

90/9.8 = 9,18s

Looking at the answers there isn't 9.18 offered as answer. But it is indeed answer for the question that has been asked. Maybe you thought that 49m/s is vertical speed than the answer would be 49/9.8=5

Answer 2

The projectile will take about 9 s to reach the highest point in its path.

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Further explanation

Acceleration is rate of change of velocity.

$\boxed {a = \frac{v - u}{t} }$

$\boxed {d = \frac{v + u}{2}~t }$

where:

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

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Let's recall Range of Projectile formula as follows:

$\boxed{ R = \frac{ v_o^2 \sin 2\theta}{g} }$

where:

R = range of projectile ( m )

v₀ = initial speed of projectile ( m/s )

θ = angle of projection

g = gravitational acceleration ( m/s² )

Let us now tackle the problem!

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Given:

initial vertical component of speed of projectile = u_y = 90 m/s

initial horizontal component of speed of projectile = u_x = 49 m/s

gravitational acceleration = g = 9.80 m/s²

Asked:

time taken to reach the highest point = t = ?

Solution:

As we know that the final vertical component of speed of projectile at the highest point is 0 m/s , therefore:

$v_y = u_y - gt$

$0 = 90 - 9.8t$

$90 = 9.8t$

$t = 90 \div 9.8$

$t \approx 9 \texttt{ s}$

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Learn more

• Velocity of Runner : https://brainly.com/question/3813437
• Kinetic Energy : https://brainly.com/question/692781
• Acceleration : https://brainly.com/question/2283922
• The Speed of Car : https://brainly.com/question/568302

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Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics