The height at time t is given by
h(t) = -4.91t² + 34.3t + 1
When the ball reaches maximum height, its derivative, h'(t) = 0.
That is,
-2(4.91)t+34.3 = 0
-9.82t + 34.3 = 0
t = 3.4929 s
Note that h''(t) = -9.82 (negative) which confirms that h will be maximum.
The maximum height is
hmax = -4.91(3.4929)² + 34.3(3.4929) + 1
= 60.903 m
Answer:
The ball attains maximum height in 3.5 s (nearest tenth).
The ball attains a maximum height of 60.9 m (nearest tenth)
Answer:
147.456077993 Hz
Explanation:
= Frequency of the sonar = 22 kHz
= Velocity of the whale = 4.95 m/s
v = Speed of sound in water = 1482 m/s
The difference in frequency is given by

The difference in frequency is 147.456077993 Hz
The wavelength decreases to roughly half.
(The frequency roughly doubles.)
Answer:
The initial speed of the bullet is
.
Explanation:
The collision between bullet and block is inelastic and let suppose that motion occurs on a horizontal surface, so that changes in gravitational potential energy can be neglected. Initially, the intial speed of the bullet-block system can be determined with the help of the Work-Energy Theorem and the Principle of Energy Conservation:


The initial speed of the bullet-block system is:

Now, the initial speed of the bullet is determined by applying the Principle of Momentum Conservation:

