Question

An astronaut on the moon throws a baseball upward. the astronaut is 6ft, 6 in. tall and the initial velocity of the ball is 30 ft per second. the height s of the ball in feet is given by the equation 2.7 30 6.5, 2 s ï½ ï­ t ï« t ï« where t is the number of seconds after the ball is thrown. (note: see where the initial height and initial velocity values play a role in the equation).

Answer 1

The equation is garbled and the question is missing.

I found this equation for the same statement:

S = - 2.7t ^2 + 30t + 6.5

And one question is: after how many seconds is the ball 12 feet above the moon's surface?

Given that S is the height of the ball, you just have to replace S with 12 and solve for t.

=> 12 = - 2.7 t^2 + 30t + 6.5

=> 2.7t^2 - 30t - 6.5 + 12 = 0

=> 2.7t^2 - 30t + 5.5 = 0

Now you can use the quadratic equation fo find t:

t = { 30 +/- √ [30^2) - 4(2.7)(5.5)] } / (2*2.7)

=> t = 0.186s and t = 10.925 s

Answer: after 0.186 s the ball is at 12 feet over the surface, and again 10.925 s

Answer 2

The maximum height of the baseball is about 90 feet

Further explanation

Acceleration is rate of change of velocity.

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

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

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

Given:

The height s of the ball in feet is given by the equation:

$s = -2.7t^2 + 30t + 6.5$

To find the velocity function, the above equation will be derived as follows:

$v = \frac{ds}{dt}$

$v = -2(2.7)t^{2-1} + 30$

$\boxed {v = -5.4t + 30}$

At the maximum height, the speed is 0 m/s , then:

$v = -5.4t + 30$

$0 = -5.4t + 30$

$5.4t = 30$

$t = 30 \div 5.4$

$\boxed {t = \frac{50}{9} ~ s}$

$s = -2.7t^2 + 30t + 6.5$

$s_{max} = -2.7(\frac{50}{9})^2 + 30(\frac{50}{9}) + 6.5$

$s_{max} = \frac{539}{6}$

$\large {\boxed {s_{max} \approx 90 ~ feet} }$

Learn more

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

Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle